Mathematics of Computation...Bach, Eric. Comments on search procedures for primitive roots, 1719 Comments on search procedures for primitive roots, 1719 Bailey, David, Borwein, Peter,

Mathematics of Computation

This journal publishes research articles in computational mathematics. Areas coveredinclude numerical analysis, with emphasis on the mathematical analysis and developmentof methods, computational number theory and algebra, and related fields. Table errataand reviews of books in areas related to computational mathematics are also included.

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INDEX TO VOLUME 66 (1997)

Alzer, Horst. On some inequalities for the gamma and psi functions, 373. On some inequalities for the incomplete gamma function, 771

Anderssen, Robert S. See Thamban Nair, M.

Andrade, M. G., and do Val, J. B. R. A numerical scheme based on mean value solutions for

the Helmholtz equation on triangular grids, 477Arnault, F. The Rabin-Monier theorem for Lucas pseudoprimes, 869Arnold, Douglas N., and Brezzi, Franco. Locking-free finite element methods for shells, 1Arnold, Douglas N., Falk, Richard S., and Winther, R. Preconditioning in H(div) and applica-

tions, 957Bach, Eric. Comments on search procedures for primitive roots, 1719

Bailey, David, Borwein, Peter, and Plouffe, Simon. On the rapid computation of various poly-

logarithmic constants, 903

Bailey, David H., Borwein, Jonathan M., and Crandall, Richard E. On the Khintchine constant,417

Baines, M. J. See Tourigny, Y.Balasubramanian, R., and Nagaraj, S. V. Density of Carmichael numbers with three prime fac-

tors, 1705Bean, Michael A. The practical computation of areas associated with binary quartic forms, 1269Belabas, K. A fast algorithm to compute cubic fields, 1213Ben Ghanem, Riadh, and Frappier, Clement. Spherical Bessel functions and explicit quadrature

formula, 289

Berczes, A., and Hajdu, L. Computational experiences on the distances of polynomials to irre-

ducible polynomials, 391

Berger, H., Warnecke, G., and Wendland, W. L. Analysis of a FEM/BEM coupling method for

transonic flow computations, 1407Bjørhus, Morten, and Stuart, Andrew M. Waveform relaxation as a dynamical system, 1101Bloom, Thomas, and Calvi, Jean-Paul. A continuity property of multivariate Lagrange interpo-

lation, 1561Borwein, Jonathan M. See Bailey, David H.

Borwein, Peter. See Bailey, DavidBossy, Mireille, and Talay, Denis. A stochastic particle method for the McKean-Vlasov and the

Burgers equation, 157Boyd, David W. On a problem of Byrnes concerning polynomials with restricted coefficients,

1697Bramble, James H., Lazarov, Raytcho D., and Pasciak, Joseph E. A least-squares approach based

on a discrete minus one inner product for first order systems, 935Brezzi, Franco. See Arnold, Douglas N.

Brunner, H. See Kauthen, J.-P.

Buchmann, Johannes, Jacobson, Michael J., Jr, and Teske, Edlyn. On some computational prob-

lems in finite abelian groups, 1663

Calvi, Jean-Paul. See Bloom, Thomas

Carlson, Timothy S., Dockery, Jack, and Lund, John. A sinc–collocation method for initial value

problems, 215Carstensen, Carsten. An a posteriori error estimate for a first-kind integral equation, 139

. A posteriori error estimate for the mixed finite element method, 465Carstensen, Carsten, and Plechac, Petr. Numerical solution of the scalar double-well problem

allowing microstructure, 997Chakraborty, K., Lal, A. K., and Ramakrishnan, B. Modular forms which behave like theta

series, 1169

Chalabi, Abdallah. On convergence of numerical schemes for hyperbolic conservation laws with

stiff source terms, 527

Chen, Gui-Qiang, and Liu, Jian-Guo. Convergence of difference schemes with high resolution

for conservation laws, 1027

Chou, Chung-Chiang, and Deng, Yuefan. Decomposing 40 billion integers by four tetrahedral

numbers, 893Chou, S. H. Analysis and convergence of a covolume method for the generalized Stokes problem,

85

http://www.ams.org/journal-getitem?pii=S0025-5718-97-00807-7





























http://www.ams.org/journal-getitem?pii=S0025-5718-97-00776-X


























Cockburn, Bernardo, and Gremaud, Pierre-Alain. A priori error estimates for numerical meth-

ods for scalar conservation laws. Part II: flux-splitting monotone schemes on irregular

Cartesian grids, 547Cockburn, Bernardo, Jones, Don A., and Titi, Edriss S. Estimating the number of asymptotic

degrees of freedom for nonlinear dissipative systems, 1073Cohen, G. L. Numbers whose positive divisors have small integral harmonic mean, 883Cohn, J. H. E. The Diophantine equation x4 + 1 = Dy2, 1347Conn, A. R., Gould, Nick, and Toint, Ph. L. A globally convergent Lagrangian barrier algorithm

for optimization with general inequality constraints and simple bounds, 261Couture, Raymond, and L’Ecuyer, Pierre. Distribution properties of multiply-with-carry random

number generators, 591Crandall, Richard, Dilcher, Karl, and Pomerance, Carl. A search for Wieferich and Wilson

primes, 433Crandall, Richard E. See Bailey, David H.Deng, Yuefan. See Chou, Chung-ChiangDilcher, Karl. See Crandall, Richard

Dockery, Jack. See Carlson, Timothy S.Du, Qiang, Jin, Ming, Li, T. Y., and Zeng, Z. The quasi-Laguerre iteration, 345Dubner, Harvey, and Nelson, Harry. Seven consecutive primes in arithmetic progression, 1743

Dummit, David S., Sands, Jonathan W., and Tangedal, Brett A. Computing Stark units for

totally real cubic fields, 1239Earnest, A. G., and Khosravani, Azar. Universal binary Hermitian forms, 1161Ehrich, Sven, and Mastroianni, Giuseppe. Stieltjes polynomials and Lagrange interpolation, 311Eichenauer–Herrmann, Jurgen, and Larcher, Gerhard. Average equidistribution properties of

compound nonlinear congruential pseudorandom numbers, 363

Eichenauer–Herrmann, Jurgen, and Niederreiter, Harald. Inversive congruential pseudorandom

numbers: distribution of triples, 1629

El-Daou, M. K., and Khajah, H. G. Iterated solutions of linear operator equations with the Tau

method, 207

Ernvall, R., and Metsankyla, T. On the p-divisibility of Fermat quotients, 1353Falk, Richard S. See Arnold, Douglas N.Fassbender, Heike. On numerical methods for discrete least-squares approximation by trigono-

metric polynomials, 719Fieker, C., Jurk, A., and Pohst, M. On solving relative norm equations in algebraic number

fields, 399Fischer, Bernd, and Prestin, Jurgen. Wavelets based on orthogonal polynomials, 1593

Forbes, Tony. A large pair of twin primes, 451Frappier, Clement. See Ben Ghanem, Riadh

Froes Bunchaft, M. E. Some extensions of the Lanczos-Ortiz theory of canonical polynomials in

the Tau Method, 609Gaal, Istvan, and Pohst, Michael. Power integral bases in a parametric family of totally real

cyclic quintics, 1689Gelb, Anne. The resolution of the Gibbs phenomenon for spherical harmonics, 699Goldman, Ron. See Lodha, Suresh K.

Gould, Nick. See Conn, A. R.Gremaud, Pierre-Alain. See Cockburn, Bernardo

Gu, Jinsheng, and Hu, Xiancheng. Extension theorems for plate elements with applications, 1375

Guo, Wen, and Stynes, Martin. An analysis of a cell-vertex finite volume method for a parabolic

convection-diffusion problem, 105

Habsieger, Laurent, and Salvy, Bruno. On integer Chebyshev polynomials, 763Hajdu, L. See Berczes, A.Hegland, Markus. See Thamban Nair, M.

Helou, Charles. On Wendt’s determinant, 1341Hofmann, Norbert, and Mathe, Peter. On quasi-Monte Carlo simulation of stochastic differential

equations, 573Horst, Reiner. On generalized bisection of n–simplices, 691Hu, Xiancheng. See Gu, Jinsheng



























































Hunter, Simon, and Sorenson, Jonathan. Approximating the number of integers free of large

prime factors, 1729Iserles, Arieh. See Paz Calvo, MariJacobson, Michael J., Jr. See Buchmann, JohannesJin, Ming. See Du, Qiang

Jones, Don A. See Cockburn, BernardoJurk, A. See Fieker, C.Kahan, William, and Li, Ren-Cang. Composition constants for raising the orders of unconven-

tional schemes for ordinary differential equations, 1089Kauthen, J.-P., and Brunner, H. Continuous collocation approximations to solutions of first kind

Volterra equations, 1441Khajah, H. G. See El-Daou, M. K.Khosravani, Azar. See Earnest, A. G.

Knyazev, Andrew V. New estimates for Ritz vectors, 985Koyama, Kenji, Tsuruoka, Yukio, and Sekigawa, Hiroshi. On searching for solutions of the Dio-

phantine equation x3 + y3 + z3 = n, 841L’Ecuyer, Pierre. See Couture, RaymondLal, A. K. See Chakraborty, K.Larcher, Gerhard. See Eichenauer–Herrmann, Jurgen

Laurie, Dirk P. Calculation of Gauss-Kronrod quadrature rules, 1133Lazarov, Raytcho D. See Bramble, James H.Lehman, Larry. Rational eigenvectors in spaces of ternary forms, 833Li, Ren-Cang. See Kahan, WilliamLi, T. Y. See Du, QiangLiu, Hailiang, and Wang, Jinghua. Decay rate for perturbations of stationary discrete shocks for

convex scalar conservation laws, 69Liu, Jian-Guo. See Chen, Gui-Qiang

Lodha, Suresh K., and Goldman, Ron. A unified approach to evaluation algorithms for multi-

variate polynomials, 1521

Louboutin, Stephane. Computation of relative class numbers of CM-fields, 1185Lukes, Richard F., Scheidler, Renate, and Williams, Hugh C. Further tabulation of the Erdos-

Selfridge function, 1709Lund, John. See Carlson, Timothy S.

MacDonald, D. A. On the highly accurate summation of certain series occurring in plate contact

problems, 1619Maltby, Roy. Pure product polynomials and the Prouhet-Tarry-Escott problem, 1323

Mastroianni, Giuseppe. See Ehrich, SvenMathe, Peter. See Hofmann, Norbert

Mattman, Thomas, and McKay, John. Computation of Galois groups over function fields, 823McKay, John. See Mattman, ThomasMeerbergen, Karl, and Spence, Alastair. Implicitly restarted Arnoldi with purification for the

shift-invert transformation, 667Melman, A. A unifying convergence analysis of second-order methods for secular equations, 333Metsankyla, T. See Ernvall, R.

Mørken, Knut, and Scherer, Karl. A general framework for high-accuracy parametric interpola-

tion, 237Morton, K. W., Stynes, Martin, and Suli, Endre. Analysis of a cell–vertex finite volume method

for convection–diffusion problems, 1389Muller, Jurgen. Accelerated polynomial approximation of finite order entire functions by growth

reduction, 743Nagao, Koh-ichi. Construction of high-rank elliptic curves with a nontrivial torsion point, 411Nagaraj, S. V. See Balasubramanian, R.

Nelson, Harry. See Dubner, Harvey

Ni, Q., and Yuan, Y. A subspace limited memory quasi-Newton algorithm for large-scale non-

linear bound constrained optimization, 1509Niederreiter, Harald. See Eichenauer–Herrmann, JurgenOmrani, A., and Shokrollahi, A. Computing irreducible representations of supersolvable groups

over small finite fields, 779




























































Osipenko, K. Yu., and Wilderotter, K. Optimal information for approximating periodic analytic

functions, 1579Paolini, Maurizio. A quasi-optimal error estimate for a discrete singularly perturbed approxima-

tion to the prescribed curvature problem, 45Pappalardi, Francesco. On the r-rank Artin Conjecture, 853Pasciak, Joseph E. See Bramble, James H.Paz Calvo, Mari, Iserles, Arieh, and Zanna, Antonella. Numerical solution of isospectral flows,

1461

Pena, J. M. B-splines and optimal stability, 1555Plechac, Petr. See Carstensen, CarstenPlouffe, Simon. See Bailey, David

Pohst, M. See Fieker, C.Pohst, Michael. See Gaal, Istvan

Pomerance, Carl. See Crandall, RichardPowell, Corey. Bounds for multiplicative cosets over fields of prime order, 807Prestin, Jurgen. See Fischer, Bernd

Ramakrishnan, B. See Chakraborty, K.Salvy, Bruno. See Habsieger, LaurentSands, Jonathan W. See Dummit, David S.

Scheidler, Renate. See Lukes, Richard F.Scherer, Karl. See Mørken, KnutSchira, Thomas. The remainder term for analytic functions of symmetric Gaussian quadratures,

297Sekigawa, Hiroshi. See Koyama, KenjiSerra, Stefano. Optimal, quasi–optimal and superlinear band–Toeplitz preconditioners for asymp-

totically ill–conditioned positive definite Toeplitz systems, 651Shokrollahi, A. See Omrani, A.

Silverman, Joseph H. Computing canonical heights with little (or no) factorization, 787Sloan, I. H., and Wozniakowski, H. An intractability result for multiple integration, 1119

Sorenson, Jonathan. See Hunter, Simon

Spence, Alastair. See Meerbergen, KarlStuart, Andrew M. See Bjørhus, MortenStynes, Martin. See Guo, Wen

. See Morton, K. W.Suli, Endre. See Morton, K. W.Suri, Manil. A reduced constraint hp finite element method for shell problems, 15Talay, Denis. See Bossy, MireilleTang, Tao, and Teng, Zhen–huan. Viscosity methods for piecewise smooth solutions to scalar

conservation laws, 495Tangedal, Brett A. See Dummit, David S.

Teng, Zhen–huan. See Tang, Tao

Teske, Edlyn. See Buchmann, JohannesThamban Nair, M., Hegland, Markus, and Anderssen, Robert S. The trade–off between regularity

and stability in Tikhonov regularization, 193

Tilli, Paolo. On the asymptotic spectrum of Hermitian block Toeplitz matrices with Toeplitz

blocks, 1147

Titi, Edriss S. See Cockburn, Bernardo

Toint, Ph. L. See Conn, A. R.Tollis, Emmanuel. Zeros of Dedekind zeta functions in the critical strip, 1295Tourigny, Y., and Baines, M. J. Analysis of an algorithm for generating locally optimal meshes

for L2 approximation by discontinuous piecewise polynomials, 623Tsuruoka, Yukio. See Koyama, Kenji

do Val, J. B. R. See Andrade, M. G.Wan, Daqing. Generators and irreducible polynomials over finite fields, 1195Wang, Jinghua. See Liu, Hailiang

Warnecke, G. See Berger, H.Wasilkowski, Grzegorz W., and Wozniakowski, Henryk. The exponent of discrepancy is at most

1.4778 . . . , 1125


























































Wei, Musheng. Equivalent formulae for the supremum and stability of weighted pseudoinverses,1487

Wendland, W. L. See Berger, H.Wilderotter, K. See Osipenko, K. Yu.Williams, H. C. (for the editors). Daniel Shanks (1917–1996), 929Williams, Hugh C. See Lukes, Richard F.Winther, R. See Arnold, Douglas N.Wozniakowski, H. See Sloan, I. H.

Wozniakowski, Henryk. See Wasilkowski, Grzegorz W.Xu, Jinchao, and Zhang, Sheng. Preconditioning the Poincare-Steklov operator by using Green’s

function, 125Yuan, Y. See Ni, Q.Yui, Noriko, and Zagier, Don. On the singular values of Weber modular functions, 1645Zagier, Don. See Yui, NorikoZanna, Antonella. See Paz Calvo, MariZeng, Z. See Du, Qiang

Zhang, Shangyou, and Zhang, Zhimin. Treatments of discontinuity and bubble functions in the

multigrid method, 1055Zhang, Sheng. See Xu, Jinchao

Zhang, Zhimin. See Zhang, ShangyouZhou, Guohui. How accurate is the streamline diffusion finite element method?, 31





















INDEX OF REVIEWS BY AUTHOR OF WORK REVIEWED

Author

Review

Number Classification Page

Adams, Loyce, &Nazareth, J. L. (Editors)

25 65F10, 65K10 1760

Ainsworth, M., Levesley, J.,

Light, W. A., &Marletta, M.

17 65-02, 65Lxx, 65Mxx 1372

Bjorck, Ake 26 65K10 1762

Brenan, K. E., Campbell, S. L.,& Petzold, L. R.

24 65Lxx, 65L06 1759

Buschman, R. G. 27 11–00 1763

Campbell, S. L. 24 See Brenan, K. E. 1759

Chaitin-Chatelin, Francoise,

& Fraysse, Valerie

19 65–02, 65G05 1751

Davy, John R., &Dew, Peter M. (Editors)

8 68Q05, 68–06 918

Debnath, L. 4 44-01, 42A38, 44A10, 44A15, 44A20, 33C10,

33C25 460

8 See Davy, John R. 918

Diaz, J.-I., & Lions, J.-L.(Editors)

9 86-06 918

Engl, Heinz W., &

Rundell, William (Editors)

2 35R30 458

Fornberg, Bengt 23 41A05, 41A10, 42A15, 65D05, 65M70,65T10 1758

Fraysse, Valerie 19 See Chaitin-Chatelin, Francoise 1751

Gautschi, Walter (Editor) 13 65-06, 11-06, 11Yxx 1367

Hackbusch, Wolfgang 22 65–00, 65–01 1756

Higham, Nicholas J. 20 65F05, 65G05, 65F10, 65F35 1753

Iserles, A. (Managing Editor) 5 65-02 915

Joe, S. 3 See Sloan, I. H. 459

Kelley, C. T. 10 65F10, 65H10, 65H20 920

Kowalski, Marek A.,

Sikorski, Krszysztof A., &Stenger, Frank

18 41-00 1374

Levesley, J. 17 See Ainsworth, M. 1372

Light, W. A. 17 See Ainsworth, M. 1372

9 See Diaz, J.-I. 918

Marletta, M. 17 See Ainsworth, M. 1372

Mayers, D. F. 6 See Morton, K. W. 916

Mollin, Richard A. 11 11R11, 11R29, 11Y40 921

Morton, K. W., &Mayers, D. F.

6 65-01, 65M06, 65N06 916

25 See Adams, Loyce 1760

Nicely, Thomas R. 12 11A41, 11-04, 11N36, 11Y60, 68M15 924

Petzold, L. R. 24 See Brenan, K. E. 1759

Quartapelle, L. 16 76-02, 76D05, 76Mxx, 65Mxx 1371

INDEX OF REVIEWS BY AUTHOR OF WORK REVIEWED

2 See Engl, Heinz W. 458

Sikorski, Krszysztof A. 18 See Kowalski, Marek A. 1374

Sloan, I. H., & Joe, S. 3 65-02, 45A55, 65D32, 65D30 459

Stenger, Frank 18 See Kowalski, Marek A. 1374

Stewart, G. W. 14 65-01 1368

Temam, Roger 15 76-02, 65M60 1369

Uberhuber, Christoph 7 65-01 917

Vajtersic, Marian 21 65N06, 65-04 1754

Wahlbin, Lars B. 1 65N30, 65N15 457

INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

Author

Review

Number Title Page

11-XX Number theory

11–00 General reference works

Buschman, R. G. 27 Number-theoretic function products 1763

11-04 Explicit machine computation and programs

Nicely, Thomas R. 12 Enumeration to 1014 of the twin primes andBrun’s constant 924

11-06 Proceedings, conferences, collections, etc.

Gautschi, Walter (Editor) 13 Mathematics of Computation 1943–1993:A half-century of computational mathe-matics 1367

11A41 Primes


11N36 Applications of sieve methods


11R11 Quadratic extensions

Mollin, Richard A. 11 Quadratics 921

11R29 Class numbers, class groups, discriminants


11Yxx Computational number theory


11Y40 Algebraic number theory computations


11Y60 Evaluation of constants



33-XX Special functions

33C10 Bessel and Airy functions, cylinder functions, 0F1

Debnath, L. 4 Integral transforms and their applications 460

35-XX Partial differential equations

35R30 Inverse problems (undetermined coefficients, etc.) for PDE

Engl, Heinz W., &

Rundell, William (Editors)

2 Inverse problems in diffusion processes 458

41-XX Approximations and expansions

41-00 General reference works

Kowalski, Marek A.,Sikorski, Krszysztof A., &Stenger, Frank

18 Selected topics in approximation and com-putation 1374

41A05 Interpolation

Fornberg, Bengt 23 A practical guide to pseudospectral meth-ods 1758

41A10 Approximation by polynomials


42-XX Fourier analysis

42A15 Trigonometric interpolation


42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type


44-XX Integral transforms, operational calculus

44-01 Instructional exposition (textbooks, tutorial papers, etc.)


44A10 Laplace transform


44A15 Special transforms (Legendre, Hilbert, etc.)


44A20 Transforms of special functions


65-XX Numerical analysis

65–00 General reference works

Hackbusch, Wolfgang 22 Integral equations: Theory and numericaltreatment 1756

65-01 Instructional exposition (textbooks, tutorial papers, etc.)

Hackbusch, Wolfgang 22 Integral equations: Theory and numerical

treatment 1756


6 Numerical solution of partial differentialequations 916

Stewart, G. W. 14 Afternotes on numerical analysis 1368

Uberhuber, Christoph 7 Computer Numerik 1, 2 917


65-02 Research exposition (monographs, survey articles)

Ainsworth, M., Levesley, J.,Light, W. A., &Marletta, M.

17 Theory and numerics of ordinary andpartial differential equations 1372

Chaitin-Chatelin, Francoise,

& Fraysse, Valerie

19 Lectures on finite precision computations 1751

Iserles, A. (Managing Editor) 5 Acta numerica 1995 915

Sloan, I. H., & Joe, S. 3 Lattice methods for multiple integration 459

65-04 Explicit machine computation and programs

Vajtersic, Marian 21 Algorithms for elliptic problems: Efficientsequential and parallel solvers 1754



65D05 Interpolation

Fornberg, Bengt 23 A practical guide to pseudospectral meth-

ods 1758

65D30 Numerical integration


65D32 Quadrature and cubature formulas


65F05 Direct methods for linear systems and matrix inversion

Higham, Nicholas J. 20 Accuracy and stability of numerical algo-rithms 1753

65F10 Iterative methods for linear systems


25 Linear and nonlinear conjugate gradient-related methods 1760

Higham, Nicholas J. 20 Accuracy and stability of numerical algo-

rithms 1753

Kelley, C. T. 10 Iterative methods for linear and nonlinearequations 920

65F35 Matrix norms, conditioning, scaling

Higham, Nicholas J. 20 Accuracy and stability of numerical algo-rithms 1753

65G05 Roundoff error

Chaitin-Chatelin, Francoise,& Fraysse, Valerie

19 Lectures on finite precision computations 1751

Higham, Nicholas J. 20 Accuracy and stability of numerical algo-

rithms 1753

65H10 Systems of equations


65H20 Global methods, including homotopy approaches



65K10 Optimization and variational techniques


25 Linear and nonlinear conjugate gradient-related methods 1760

Bjorck, Ake 26 Numerical methods for least squares prob-lems 1762

65Lxx Ordinary differential equations



17 Theory and numerics of ordinary and

partial differential equations 1372


24 Numerical solution of initial-value problemsin differential-algebraic equations 1759

65L06 Multistep, Runge-Kutta and extrapolation methods


24 Numerical solution of initial-value problemsin differential-algebraic equations 1759

65Mxx Partial differential equations, initial value and time-dependent

initial-boundary value problems



17 Theory and numerics of ordinary and

partial differential equations 1372

Quartapelle, L. 16 Numerical solution of the incompressibleNavier-Stokes equations 1371

65M06 Finite difference methods



65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Temam, Roger 15 Navier-Stokes equations and nonlinear func-tional analysis 1369

65M70 Spectral, collocation and related methods


65N06 Finite difference methods



Vajtersic, Marian 21 Algorithms for elliptic problems: Efficientsequential and parallel solvers 1754

65N15 Error bounds

Wahlbin, Lars B. 1 Superconvergence in Galerkin finite elementmethods 457

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Wahlbin, Lars B. 1 Superconvergence in Galerkin finite elementmethods 457

65T10 Trigonometric approximation and interpolation



68-XX Computer science

68–06 Proceedings, conferences, collections, etc.


8 Abstract machine models for highly parallelcomputers 918

68M15 Reliability and testing


68Q05 Models of computation (abstract processors, Turing machines, etc.)


8 Abstract machine models for highly parallelcomputers 918

76-XX Fluid mechanics

76-02 Research exposition (monographs, survey articles)


Temam, Roger 15 Navier-Stokes equations and nonlinear func-tional analysis 1369

76D05 Navier-Stokes equations


76Mxx Basic methods in fluid mechanics


86-XX Geophysics


Diaz, J.-I., & Lions, J.-L.(Editors)

9 Mathematics, climate and environment 918

INDEX OF ERRATA

No. Author Title Page

632 Byrd, P. F., &

Friedman, M. D.

Handbook of elliptic integrals for engineers and

scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1767

631 Magnus, W.,Oberhettinger, F., &

Tricomi, F. G.(research

associates)Erdelyi, A.(Editor) (Editor)

Tables of integral transforms, Vol. I . . . . . . . . . 1766

628 Gradshteyn, I. S., &

Ryzhik, I. M.Table of integrals, series, and products . . . . . . 463

629 Prudnikov, A. P.,Brychkov, Yu. A., &Marichev, O. I.

Integrals and series, Vol. 1, Elementary func-tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1765

630 Prudnikov, A. P.,Brychkov, Yu. A., &Marichev, O. I.

Integrals and series, Vol. 4, Direct Laplacetransforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1766




INDEX OF SUPPLEMENTS

INDEX OF CORRIGENDA

Jakubec, Stanislav and

Marko, Frantisekand Szymiczek,

Kazimierz

Parity of class numbers and Witt equivalence of quartic

fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927

Woznicki, Zbigniew The Sigma-SOR algorithm and the optimal strategy forthe utilization of the SOR iterative method . . . . . . . 1769

INDEX OF SUPPLEMENTS

Conn, A .R.,Gould, Nick, &Toint, Ph. L.

A globally convergent Lagrangian barrier algorithm foroptimization with general inequality constraints andsimple bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan.



OMPUTATIONM

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ATHEMATICS

A M E R I C A N M A T H E M A T I C A L S O C I E T Y

VOLUME 66 1997ΑΓ

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PROVIDENCE, RHODE ISLAND USA

ISSN 0025-5718

EDITED BY

James H. Bramble

Susanne C. Brenner

Arjeh M. Cohen

Howard Elman

Richard S. Falk

Walter Gautschi

Daniel W. Lozier

James N. Lyness

Roswitha März

Harald Niederreiter

Andrew M. Odlyzko

John E. Osborn

Stanley Osher

Carl Pomerance

René Schoof

L. Ridgway Scott

Chi-Wang Shu

Frank Stenger

Hans J. Stetter

G. W. Stewart

Nico M. Temme

Vidar Thomée

Lars B. Wahlbin, Managing Editor

Joseph D. Ward

Hugh C. Williams

Stephen J. Wright

Mathematics of Computation

This journal publishes research articles in computational mathematics. Areas coveredinclude numerical analysis, with emphasis on the mathematical analysis and developmentof methods, computational number theory and algebra, and related fields. Table errataand reviews of books in areas related to computational mathematics are also included.

Submission information. See Information for Authors at the end of this issue.

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Subscription information. Mathematics of Computation is published quarterly. Be-ginning in January 1996 Mathematics of Computation is accessible from e-MATH via theWorld Wide Web at the URL http : //www.ams.org/publications/. Subscription pricesfor Volume 66 (1997) are as follows: for paper delivery, $307 list, $246 institutional mem-ber, $276 corporate member, $200 MAA & SIAM members; $184 individual member; forelectronic delivery, $276 list, $221 institutional member, $248 corporate member, $179MAA & SIAM members, $166 individual member; for combination paper and electronicdelivery, $353 list, $282 insititutional member, $318 corporate member, $229 MAA &SIAM members, $212 individual member. If ordering the paper version, add $12 for sur-face delivery outside the United States and India; $18 to India. Expedited delivery todestinations in North America is $17; elsewhere $49.

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MATHEMATICS OF COMPUTATION

CONTENTS

Vol. 66, No. 217 January 1997

Douglas N. Arnold and Franco Brezzi, Locking-free finite elementmethods for shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Manil Suri, A reduced constraint hp finite element method for shell problems 15

Guohui Zhou, How accurate is the streamline diffusion finite elementmethod? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Maurizio Paolini, A quasi-optimal error estimate for a discrete singularlyperturbed approximation to the prescribed curvature problem . . . . . . . 45

Hailiang Liu and Jinghua Wang, Decay rate for perturbations ofstationary discrete shocks for convex scalar conservation laws . . . . . . . . . 69

S. H. Chou, Analysis and convergence of a covolume method for thegeneralized Stokes problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Wen Guo and Martin Stynes, An analysis of a cell-vertex finite volumemethod for a parabolic convection-diffusion problem . . . . . . . . . . . . . . . . . . 105

Jinchao Xu and Sheng Zhang, Preconditioning the Poincare-Steklovoperator by using Green’s function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Carsten Carstensen, An a posteriori error estimate for a first-kind integralequation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Mireille Bossy and Denis Talay, A stochastic particle method for theMcKean-Vlasov and the Burgers equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

M. Thamban Nair, Markus Hegland, and Robert S. Anderssen, Thetrade–off between regularity and stability in Tikhonov regularization . 193

M. K. El-Daou and H. G. Khajah, Iterated solutions of linear operatorequations with the Tau method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Timothy S. Carlson, Jack Dockery, and John Lund, A sinc–collocationmethod for initial value problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Knut Mørken and Karl Scherer, A general framework for high-accuracyparametric interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

A. R. Conn, Nick Gould, and Ph. L. Toint, A globally convergentLagrangian barrier algorithm for optimization with general inequalityconstraints and simple bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Riadh Ben Ghanem and Clement Frappier, Spherical Bessel functionsand explicit quadrature formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Thomas Schira, The remainder term for analytic functions of symmetricGaussian quadratures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Sven Ehrich and Giuseppe Mastroianni, Stieltjes polynomials andLagrange interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

A. Melman, A unifying convergence analysis of second-order methods forsecular equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

Qiang Du, Ming Jin, T.Y. Li, and Z. Zeng, The quasi-Laguerre iteration 345

Jurgen Eichenauer–Herrmann and Gerhard Larcher, Average equidis-tribution properties of compound nonlinear congruential pseudorandomnumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Horst Alzer, On some inequalities for the gamma and psi functions . . . . . . 373












































A. Berczes and L. Hajdu, Computational experiences on the distances ofpolynomials to irreducible polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

C. Fieker, A. Jurk, and M. Pohst, On solving relative norm equations inalgebraic number fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

Koh-ichi Nagao, Construction of high-rank elliptic curves with a nontrivialtorsion point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

David H. Bailey, Jonathan M. Borwein, and Richard E. Crandall, Onthe Khintchine constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Richard Crandall, Karl Dilcher, and Carl Pomerance, A search forWieferich and Wilson primes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

Tony Forbes, A large pair of twin primes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

Reviews and Descriptions of Tables and Books . . . . . . . . . . . . . . . . . . . . . 457

Wahlbin 1, Engl and Rundell, Editors 2, Sloan and Joe 3, Debnath 4

Table Errata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

Supplement to “A globally convergent Lagrangian barrier algorithm foroptimization with general inequality constraints and simple bounds” byA. R. Conn, Nick Gould, and Ph. L. Toint . . . . . . . . . . . . . . . . . . . . . S1

Vol. 66, No. 218 April 1997

Carsten Carstensen, A posteriori error estimate for the mixed finite elementmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

M. G. Andrade and J. B. R. do Val, A numerical scheme based on meanvalue solutions for the Helmholtz equation on triangular grids . . . . . . . . 477

Tao Tang and Zhen–huan Teng, Viscosity methods for piecewise smoothsolutions to scalar conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

Abdallah Chalabi, On convergence of numerical schemes for hyperbolicconservation laws with stiff source terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

Bernardo Cockburn and Pierre-Alain Gremaud, A priori errorestimates for numerical methods for scalar conservation laws. Part II:flux-splitting monotone schemes on irregular Cartesian grids . . . . . . . . . 547

Norbert Hofmann and Peter Mathe, On quasi-Monte Carlo simulation ofstochastic differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

Raymond Couture and Pierre L’Ecuyer, Distribution properties ofmultiply-with-carry random number generators . . . . . . . . . . . . . . . . . . . . . . . 591

M. E. Froes Bunchaft, Some extensions of the Lanczos-Ortiz theory ofcanonical polynomials in the Tau Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

Y. Tourigny and M. J. Baines, Analysis of an algorithm for generatinglocally optimal meshes for L2 approximation by discontinuous piecewisepolynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

Stefano Serra, Optimal, quasi–optimal and superlinear band–Toeplitzpreconditioners for asymptotically ill–conditioned positive definiteToeplitz systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

Karl Meerbergen and Alastair Spence, Implicitly restarted Arnoldi withpurification for the shift-invert transformation . . . . . . . . . . . . . . . . . . . . . . . . 667








































Reiner Horst, On generalized bisection of n–simplices . . . . . . . . . . . . . . . . . . . . 691

Anne Gelb, The resolution of the Gibbs phenomenon for sphericalharmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699

Heike Fassbender, On numerical methods for discrete least-squaresapproximation by trigonometric polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 719

Jurgen Muller, Accelerated polynomial approximation of finite order entirefunctions by growth reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743

Laurent Habsieger and Bruno Salvy, On integer Chebyshev polynomials 763

Horst Alzer, On some inequalities for the incomplete gamma function . . . . 771

A. Omrani and A. Shokrollahi, Computing irreducible representations ofsupersolvable groups over small finite fields . . . . . . . . . . . . . . . . . . . . . . . . . . 779

Joseph H. Silverman, Computing canonical heights with little (or no)factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

Corey Powell, Bounds for multiplicative cosets over fields of prime order . 807

Thomas Mattman and John McKay, Computation of Galois groups overfunction fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823

Larry Lehman, Rational eigenvectors in spaces of ternary forms . . . . . . . . . . 833

Kenji Koyama, Yukio Tsuruoka, and Hiroshi Sekigawa, On searchingfor solutions of the Diophantine equation x3 + y3 + z3 = n . . . . . . . . . . . 841

Francesco Pappalardi, On the r-rank Artin Conjecture . . . . . . . . . . . . . . . . . . 853

F. Arnault, The Rabin-Monier theorem for Lucas pseudoprimes . . . . . . . . . . 869

G. L. Cohen, Numbers whose positive divisors have small integral harmonicmean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883

Chung-Chiang Chou and Yuefan Deng, Decomposing 40 billion integersby four tetrahedral numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893

David Bailey, Peter Borwein, and Simon Plouffe, On the rapidcomputation of various polylogarithmic constants . . . . . . . . . . . . . . . . . . . . 903


Iserles, Managing Editor 5, Morton and Mayers 6, Uberhuber 7,Davy and Dew, Editors 8, Diaz and Lions, Editors 9, Kelley 10,Mollin 11, Nicely 12

Corrigendum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927

Vol. 66, No. 219 July 1997

Daniel Shanks (1917–1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929

James H. Bramble, Raytcho D. Lazarov, and Joseph E. Pasciak, Aleast-squares approach based on a discrete minus one inner product forfirst order systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935

Douglas N. Arnold, Richard S. Falk, and R. Winther, Preconditioningin H (div) and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957

Andrew V. Knyazev, New estimates for Ritz vectors . . . . . . . . . . . . . . . . . . . . 985

Carsten Carstensen and Petr Plechac, Numerical solution of the scalardouble-well problem allowing microstructure . . . . . . . . . . . . . . . . . . . . . . . . . 997






































Gui-Qiang Chen and Jian-Guo Liu, Convergence of difference schemeswith high resolution for conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027

Shangyou Zhang and Zhimin Zhang, Treatments of discontinuity andbubble functions in the multigrid method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055

Bernardo Cockburn, Don A. Jones, and Edriss S. Titi, Estimatingthe number of asymptotic degrees of freedom for nonlinear dissipativesystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073

William Kahan and Ren-Cang Li, Composition constants for raising theorders of unconventional schemes for ordinary differential equations . . 1089

Morten Bjørhus and Andrew M. Stuart, Waveform relaxation as adynamical system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1101

I. H. Sloan and H. Wozniakowski, An intractability result for multipleintegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119

Grzegorz W. Wasilkowski and Henryk Wozniakowski, The exponent ofdiscrepancy is at most 1.4778 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125

Dirk P. Laurie, Calculation of Gauss-Kronrod quadrature rules . . . . . . . . . . 1133

Paolo Tilli, On the asymptotic spectrum of Hermitian block Toeplitzmatrices with Toeplitz blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147

A. G. Earnest and Azar Khosravani, Universal binary Hermitian forms 1161

K. Chakraborty, A. K. Lal, and B. Ramakrishnan, Modular formswhich behave like theta series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169

Stephane Louboutin, Computation of relative class numbers of CM-fields 1185

Daqing Wan, Generators and irreducible polynomials over finite fields . . . . 1195

K. Belabas, A fast algorithm to compute cubic fields . . . . . . . . . . . . . . . . . . . . . 1213

David S. Dummit, Jonathan W. Sands, and Brett A. Tangedal,Computing Stark units for totally real cubic fields . . . . . . . . . . . . . . . . . . . 1239

Michael A. Bean, The practical computation of areas associated with binaryquartic forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1269

Emmanuel Tollis, Zeros of Dedekind zeta functions in the critical strip . . 1295

Roy Maltby, Pure product polynomials and the Prouhet-Tarry-Escottproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323

Charles Helou, On Wendt’s determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1341

J. H. E. Cohn, The Diophantine equation x4 + 1 = Dy2 . . . . . . . . . . . . . . . . . 1347

R. Ernvall and T. Metsankyla, On the p-divisibility of Fermat quotients 1353


Gautschi, Editor 13, Stewart 14, Temam 15, Quartapelle 16, Ainsworth,Levesley, Light, and Marletta 17, Kowalski, Sikorski, and Stenger 18

Vol. 66, No. 220 October 1997

Jinsheng Gu and Xiancheng Hu, Extension theorems for plate elementswith applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1375

K. W. Morton, Martin Stynes, and Endre Suli, Analysis of a cell–vertexfinite volume method for convection–diffusion problems . . . . . . . . . . . . . . . 1389







































H. Berger, G. Warnecke, and W. L. Wendland, Analysis of aFEM/BEM coupling method for transonic flow computations . . . . . . . . . 1407

J.-P. Kauthen and H. Brunner, Continuous collocation approximations tosolutions of first kind Volterra equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1441

Mari Paz Calvo, Arieh Iserles, and Antonella Zanna, Numericalsolution of isospectral flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1461

Musheng Wei, Equivalent formulae for the supremum and stability ofweighted pseudoinverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1487

Q. Ni and Y. Yuan, A subspace limited memory quasi-Newton algorithm forlarge-scale nonlinear bound constrained optimization . . . . . . . . . . . . . . . . . 1509

Suresh K. Lodha and Ron Goldman, A unified approach to evaluationalgorithms for multivariate polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1521

J.M. Pena, B-splines and optimal stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555

Thomas Bloom and Jean-Paul Calvi, A continuity property ofmultivariate Lagrange interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1561

K. Yu. Osipenko and K. Wilderotter, Optimal information forapproximating periodic analytic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1579

Bernd Fischer and Jurgen Prestin, Wavelets based on orthogonalpolynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1593

D.A. MacDonald, On the highly accurate summation of certain seriesoccurring in plate contact problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1619

Jurgen Eichenauer–Herrmann and Harald Niederreiter, Inversivecongruential pseudorandom numbers: distribution of triples . . . . . . . . . . . 1629

Noriko Yui and Don Zagier, On the singular values of Weber modularfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1645

Johannes Buchmann, Michael J. Jacobson, Jr., and Edlyn Teske, Onsome computational problems in finite abelian groups . . . . . . . . . . . . . . . . 1663

Istvan Gaal and Michael Pohst, Power integral bases in a parametricfamily of totally real cyclic quintics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1689

David W. Boyd, On a problem of Byrnes concerning polynomials withrestricted coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1697

R. Balasubramanian and S. V. Nagaraj, Density of Carmichael numberswith three prime factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1705

Richard F. Lukes, Renate Scheidler, and Hugh C. Williams, Furthertabulation of the Erdos-Selfridge function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1709

Eric Bach, Comments on search procedures for primitive roots . . . . . . . . . . . 1719

Simon Hunter and Jonathan Sorenson, Approximating the number ofintegers free of large prime factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1729

Harvey Dubner and Harry Nelson, Seven consecutive primes inarithmetic progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1743


Chaitin-Chatelin and Fraysse 19, Higham 20, Vajtersic 21, Hackbusch22, Fornberg 23, Brenan, Campbell, and Petzold 24, Adams andNazareth, Editors 25, Bjorck 26, Buschman 27










































Table Errata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1765

Corrigendum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1769

Editorial Information

As of July 31, 1997, the backlog for this journal was approximately 1 issue. This esti-mate is the result of dividing the number of manuscripts for this journal in the Providenceoffice that have not yet gone to the printer on the above date by the average numberof articles per issue over the previous twelve months, reduced by the number of issuespublished in six months (the time necessary for editing and composing a typical issue).

A Consent to Publish and Copyright Agreement is required before a paper will bepublished in this journal. After a paper is accepted for publication, the Providence officewill send out a Consent to Publish and Copyright Agreement to all authors of the paper.By submitting a paper to this journal, authors certify that the results have not been sub-mitted to nor are they under consideration for publication by another journal, conferenceproceedings, or similar publication.

Information for Authors

Initial submission. An author should submit three paper copies of the manuscript.Initial submission by e-mail is not allowed. The author may suggest an appropriate editorfor his paper. All contributions intended for publication and all books for review shouldbe addressed to Lars B. Wahlbin, Managing Editor, Mathematics of Computation, Centerfor Applied Mathematics, 657 Frank H. T. Rhodes Hall, Cornell University, Ithaca, NY14853-3801. The date received, which is published with the final version of an acceptedpaper, is the date received in the office of the Managing Editor, and it is the responsibilityof the author to submit manuscripts directly to this office.

The first page must consist of a descriptive title, followed by an abstract that summa-rizes the article in language suitable for workers in the general field (algebra, analysis,etc.). The descriptive title should be short, but informative; useless or vague phrasessuch as “some remarks about” or “concerning” should be avoided. The abstract mustbe brief and reasonably self-contained. Included with the footnotes to the paper, thereshould be the 1991 Mathematics Subject Classification representing the primary and sec-ondary subjects of the article. This may be followed by a list of key words and phrases

describing the subject matter of the article and taken from it. A list of classificationsmay be found in the annual index of Mathematical Reviews, published with the De-cember issue starting in 1990. Journal abbreviations used in bibliographies are alsolisted in the latest Mathematical Reviews annual index. The classifications and thejournal abbreviations are accessible from e-MATH via the World Wide Web throughthe URL http : //www.ams.org/committee/publications/mr-info.html or via FTP toe-math.ams.org (login as anonymous and enter username as password). The classifica-tions are available as a browsable list and the journal abbreviations are available througha search tool. When the manuscript is submitted, authors should supply the editor withelectronic addresses if available. These will be printed after the postal address at the endof each article.

Electronically prepared manuscripts. For the final submission of accepted papers,the AMS encourages use of electronically prepared manuscripts, with a strong preferencefor AMS-LATEX. To this end, the Society has prepared AMS-LATEX author packages foreach AMS publication. Author packages include instructions for preparing electronicmanuscripts, the AMS Author Handbook, samples, and a style file that generates theparticular design specifications of that publication series. Articles properly prepared usingthe AMS-LATEX style file automatically provide hypertext linking to the bibliography andother elements of the article for searching electronically on the World Wide Web. Becauselinking must often be added manually to electronically prepared manuscripts in otherforms of TEX, using AMS-LATEX also reduces the amount of technical intervention oncethe files are received by the AMS. This results in fewer errors in processing and savesthe author proofreading time. AMS-LATEX papers also move more efficiently through theproduction stream, helping to minimize publishing costs.

AMS-LATEX is the highly preferred format of TEX, but author packages are also availablein AMS-TEX. Those authors who make use of these style files from the beginning of the

writing process will further reduce their own efforts. Manuscripts prepared electronicallyin LATEX or plain TEX are normally not acceptable due to the high amount of technical timerequired to insure that the file will run properly through the AMS in-house productionsystem. LATEX users will find that AMS-LATEX is the same as LATEX with additionalcommands to simplify the typesetting of mathematics, and users of plain TEX should havethe foundation for learning AMS-LATEX.

Authors may retrieve an author package from e-MATH via the World Wide Webthrough the URL http : //www.ams.org/tex/ or via FTP to e-math.ams.org (login asanonymous and enter username as password). The author package can also be obtainedfree of charge by sending e-mail to [email protected] (Internet) or from the Publication Divi-sion, American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248. Whenrequesting an author package, please specify AMS-LATEX or AMS-TEX, Macintosh orIBM (3.5) format, and the publication in which your paper will appear. Please be sure toinclude your complete mailing address.

The final version of the electronic manuscript should be sent to the Providence officeimmediately after the paper has been accepted for publication. The author should alsosend the final version of the paper manuscript to the Managing Editor, who will forwarda copy to the Providence office. Editors will require authors to send their electronicallyprepared manuscripts to the Providence office in a timely fashion. Electronically preparedmanuscripts can be sent via e-mail to [email protected] (Internet) or on diskette tothe Electronic Prepress Department, American Mathematical Society, P.O. Box 6248,Providence, RI 02940-6248. When sending a manuscript electronically, please be sureto include a message indicating in which publication the paper has been accepted. Nocorrections will be accepted electronically. Authors must mark their changes on theirproof copies and return them to the Providence office. Complete instructions on how tosend files are included in the author package.

Electronic graphics. Figures may be sent to the AMS in an electronic format. TheAMS recommends that graphics created electronically be saved in Encapsulated PostScript(EPS) format. This includes graphics originated via a graphics application as well asscanned photographs or other computer-generated images.

If the graphics package used does not support EPS output, the graphics file should besaved in one of the standard graphics formats—such as TIFF, PICT, GIF, etc.—ratherthan in an application-dependent format. Graphics files sent in an application-dependentformat are not likely to be used. No matter what method was used to produce the graphic,it is necessary to provide a paper copy to the AMS.

Authors using graphics packages for the creation of electronic art should also avoid theuse of any lines thinner than 0.5 points in width. Many graphics packages allow the userto specify a “hairline” for a very thin line. Hairlines often look acceptable when proofedon a typical laser printer. However, when produced on a high-resolution laser imagesetter,hairlines become nearly invisible and will be lost entirely in the final printing process.

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or by contacting the Electronic Prepress Department, American Mathematical Society,P.O. Box 6248, Providence, RI 02940-6248. The request should include the title of thepaper, the name(s) of the author(s), the name of the publication in which the paper hasor will appear, and the volume and issue numbers if known. The TEX file will be sentto the author making the request after the article goes to the printer. If the requestor

can receive Internet e-mail, please include the e-mail address to which the file shouldbe sent. Otherwise please indicate a diskette format and postal address to which a diskshould be mailed. Note: Because TEX production at the AMS sometimes requires extrafonts and macros that are not yet publicly available, TEX files cannot be guaranteed torun through the author’s version of TEX without errors. The AMS regrets that it cannotprovide support to eliminate such errors in the author’s TEX environment.

Any inquiries concerning a paper that has been accepted for publication should be sentdirectly to the Electronic Prepress Department, American Mathematical Society, P.O. Box6248, Providence, RI 02940-6248.

Editorial Committee

ANDREW M. ODLYZKO, AT&T Bell Laboratories, 600 Mountain Avenue, MurrayHill, NJ 07974; E-mail : [email protected]

STANLEY OSHER, Department of Mathematics, University of California, Los Angeles,CA 90024; E-mail : [email protected]

G. W. STEWART, Department of Computer Science, University of Maryland, CollegePark, MD 20742; E-mail : [email protected]

LARS B. WAHLBIN, Chairman. Center for Applied Mathematics, 657 Frank H. T.Rhodes Hall, Cornell University, Ithaca, NY 14853-3801; E-mail : [email protected]

Board of Associate Editors

JAMES H. BRAMBLE, Department of Mathematics, Texas A & M University, CollegeStation, TX 77843-3368; E-mail : [email protected]

SUSANNE C. BRENNER, Department of Mathematics, University of South Carolina,Columbia, SC 29208; E-mail : [email protected]

ARJEH M. COHEN, Faculteit Wiskunde en Informatica, TU Eindhoven, Postbus 513,5600 MB Eindhoven, The Netherlands; E-mail : [email protected]

HOWARD ELMAN, Department of Computer Science, University of Maryland, CollegePark, MD 20742; E-mail : [email protected]

RICHARD S. FALK, Department of Mathematics, Rutgers University, New Brunswick,NJ 08903-2101; E-mail : [email protected]

WALTER GAUTSCHI, Department of Computer Sciences, Purdue University, WestLafayette, IN 47907; E-mail : [email protected]

DANIEL W. LOZIER, Applied and Computational Mathematics Division, NationalInstitute of Standards and Technology, Gaithersburg, MD 20899-0001; E-mail : dlozier@

nist.gov

JAMES N. LYNESS, Mathematics and Computer Science Division, Argonne NationalLaboratory, 9700 S. Cass Avenue, Argonne, IL 60439; E-mail : [email protected]

ROSWITHA MARZ, Institut fur Mathematik, Humboldt-Universitat zu Berlin, D-10099 Berlin, Germany; E-mail : [email protected]

HARALD NIEDERREITER, Institute for Information Processing, Austrian Academyof Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria; E-mail : [email protected].

ac.at

JOHN E. OSBORN, Department of Mathematics, University of Maryland, CollegePark, MD 20742; E-mail : [email protected]

CARL POMERANCE, Department of Mathematics, The University of Georgia,Athens, GA 30602; E-mail : [email protected]

RENE SCHOOF, Dipartimento di Matematica, 2a Universita di Roma “Tor Vergata”,I-00133 Roma, Italy; E-mail : [email protected]

L. RIDGWAY SCOTT, Department of Mathematics, University of Houston, Houston,TX 77204-3476; E-mail : [email protected]

CHI-WANG SHU, Applied Mathematics Division, Brown University, Providence, RI02912-0001; E-mail : [email protected]

FRANK STENGER, Department of Computer Science, University of Utah, Salt LakeCity, UT 84112; E-mail : [email protected]

HANS J. STETTER, Institut fur Numerische Mathematik, Technische UniversitatWien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria; E-mail : stetter@uranus.

tuwien.ac.at

NICO M. TEMME, Stichting Mathematisch Centrum, Centrum voor Wiskunde enInformatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands; E-mail : [email protected]

VIDAR THOMEE, Mathematics Department, Chalmers University of Technology, S-412 96 Goteborg, Sweden; E-mail : [email protected]

JOSEPH D. WARD, Department of Mathematics, Texas A & M University, CollegeStation, TX 77843-3368; E-mail : [email protected]

HUGH C. WILLIAMS, Department of Computer Science, University of Manitoba, Win-nipeg, Manitoba, Canada R3T 2N2; E-mail : Hugh [email protected]

STEPHEN J. WRIGHT, Mathematics and Computer Science Division, Argonne Na-tional Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439; E-mail : [email protected]

(Continued from back cover)

Richard F. Lukes, Renate Scheidler, and Hugh C. Williams, Furthertabulation of the Erdos-Selfridge function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1709

Eric Bach, Comments on search procedures for primitive roots . . . . . . . . . . . 1719

Simon Hunter and Jonathan Sorenson, Approximating the number ofintegers free of large prime factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1729

Harvey Dubner and Harry Nelson, Seven consecutive primes inarithmetic progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1743


Chaitin-Chatelin and Fraysse 19, Higham 20, Vajtersic 21, Hackbusch22, Fornberg 23, Brenan, Campbell, and Petzold 24, Adams andNazareth, Editors 25, Bjorck 26, Buschman 27

Table Errata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1765

Corrigendum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1769

No microfiche supplement in this issue

Documents

Mathematics of Computation...Bach, Eric. Comments on search procedures for primitive roots, 1719 Comments on search procedures for primitive roots, 1719 Bailey, David, Borwein, Peter,