Georg Heinig

November 24, 1947 – May 10, 2005

A personal memoir and appreciation

Karla Rost

Department of Mathematics, Chemnitz University of Technology,

D-09107 Chemnitz, Germany

On May 10, 2005, Georg Heinig, an excellent mathematician died unexpectedlyat the age of 57. He was a world leader in the field of structured matrices.As associate editor of the journal Linear Algebra and its Applications sincehis appointment in 1991 he contributed much to the journal’s success by hisvaluable and extensive work. In what follows I want to try to capture someaspects of this mathematical life and his personality.

Georg was born on November 24, 1947, in the small town of Zschopau inthe Ore Mountains (Erzgebirge) in East Germany. From 1954 to 1964 heattended the elementary school there. Because of his good performance he was

Email address: krost@mathematik.tu-chemnitz.de (Karla Rost).

Preprint submitted to Elsevier Science 9 September 2005

admitted to the elite school of Karl-Marx-Stadt (now Chemnitz) Universityof Technology, where he received his graduation diploma with the grade “verygood”. During his time at this school he already showed extraordinary talentfor mathematics and natural sciences, and his passion and skills for solvingmathematical problems grew.

Subsequently he studied mathematics at Karl-Marx-Stadt (now Chemnitz)University of Technology. He wrote his diploma thesis under the supervisionof Siegfried Prossdorf on some properties of normally solvable operators inBanach spaces. Some years ago S. Prossdorf told me that he liked to recallthe time he spent with the gifted and creative student Georg. In the summerof 1970 Georg received the best possible grade for the defense of his diplomathesis.

He received a scholarship to study for the Ph.D. abroad and he decided to goto the State University of Moldavia at Kishinev from 1971 to 1974. There heworked on his PhD thesis on the subject of Wiener-Hopf block operators andsingular integral operators under the supervision of Israel Gohberg [IG] whoeven then was internationally well-known and respected.

Here is a copy of the authenticated Russian document certifying Georg’s degreeas “candidate of sciences”, which is the equivalent to a PhD:

A well known, important and often cited work with I. Gohberg from this timeis the paper [112]. With great admiration and deep gratitude Georg alwaysconsidered I. Gohberg as his scientific father ([IG], page 63).

By this time Georg was cast irretrievably into the realm of matrix theory,in particular the theory of structured matrices. His commitment to this fieldover three decades has benefited several scientific grandchildren of Israel Go-hberg’s of whom I am one. Georg’s connection to I. Gohberg has never ceased.From 1993 on, he was a member of the editorial board of the journal IntegralEquations and Operator Theory.

I became acquainted with Georg when he returned to Karl-Marx-Stadt in late1974, where he worked at the Department of Mathematics, first in the group

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chaired by S. Prossdorf and then (after Prossdorf’s leave to Berlin 1975) in B.Silbermann’s group. There he found extremely good conditions. Prossdorf andSilbermann considered him as an equal partner, and hence he could pursue hisinclinations in research unhampered and even build a small research group.

In all honesty, I have to admit that I was not euphoric at my first encounterswith Georg. He was very young, with no experience as a supervisor, and inaddition, he appeared to me as too self-oriented. It was his ability to awakemy interest in the topics he proposed, which in 1975 led me to decide to writemy diploma thesis under his supervision despite my initial hesitations. In facthe turned out to be an extraordinary supervisor, and I soon became awarethat starting my scientific career with him was a lucky decision. In later yearswe managed better and better to get attuned to each other, and consequentlyI wrote a large part of my dissertation on the method of UV-reduction forinverting structured matrices under his supervision. Meanwhile 30 years offruitful and intense joint work have passed. One joint monograph and almost40 papers in journals testify to this.

In 1979 Georg defended his habilitation thesis (of an imposing length 287pages) on the spectral theory of operator bundles and the algebraic theory offinite Toeplitz matrices with excellence.

Georg was very optimistic and in love with life. I very much miss his cheerfuland bright laughter. Certainly his stay in Kishinev intensified his wanderlustand his curiosity for other countries. Despite the travel restrictions for citi-zens of the G.D.R., the former socialist part of Germany, there was scientificcooperation with Syria and Ethiopia, and Georg was offered a research andworking visit at Aleppo University in Syria in 1982. During a longer stay from1987-89 at Addis Ababa University in Ethiopia, he was accompanied by hiswife Gerti and by his two children Peter (born 1974) and Susanne (born 1977).Later on, both these stays certainly helped him to settle down in Kuwait.

Georg was well established at Karl-Marx-Stadt (now Chemnitz) Universityof Technology. He was a respected and highly recognized colleague with out-standing achievements in research and teaching. Thus Georg was appointed asa full professor for numerical mathematics at Karl Marx University of Leipzig.Since the late seventies his international recognition has grown enormously,which is, for example, reflected by the interest of the Birkhauser publishinghouse in the joint monograph [86,89], which was originally intended to bepublished by the Akademie-Verlag only.

The “Wende” in the fall of 1989 was an incisive break and turning pointin the life of many people in East Germany, and thus also for Georg. Allscientists working at universities were formally dismissed and had to apply fora position anew. An important criterion for a refusal of such an application

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was the political proximity to the old socialist system. Due to this, in 1993Georg went to Kuwait University, where he worked as a professor for morethan 10 years. He died of a heart attack on May 10, 2005, in his apartment inKuwait.

During this long period in Kuwait he continuously maintained scientific andpersonal contacts with his friends and former colleagues from Chemnitz, in-cluding Albrecht Bottcher, Bernd Silbermann, Steffen Roch, and myself. InMay 1998 we all had the opportunity to participate in the International Con-ference on Fourier Analysis and Applications in Kuwait. Georg had an es-pecially high admiration for Albrecht Bottcher and was therefore very gladthat Albrecht agreed to enter the scientific committee and the editorial boardof the proceedings of this conference [34]. In the course of that conference weconvinced ourselves with great pleasure of the respect in which Georg was heldby his colleagues and students in Kuwait. Thus he found very good friendsand supporters in his Kuwaiti colleagues Fadhel Al-Musallam and MansourAl-Zanaidi as well as in his colleague Christian Grossmann from Dresden Uni-versity of Technology, who stayed in Kuwait from 1992 to 1998. One of thehighlights of his life occurred in 2002, when the Amir of Kuwait distinguishedhim as the Researcher of the Year. Since 2004 he was also a member of theeditorial board of the Kuwait Journal of Science and Engineering.

My mathematical knowledge and my ability to tackle problems have benefitedimmensely from Georg. He had an extraordinary gift to explain complicatedthings in simple terms. This was also appreciated by his students. His lecturesand scientific talks were very sought after and well attended. The aestheticcomponent is well to the fore in his work. He mastered with equal facilityproblems of extreme generality and abstraction as well as down-to-earth ques-tions.

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Georg is the author and coauthor of more than 100 scientific publications.He always made high demands on himself and on his coauthors regarding notonly mathematical originality and exactness but also regarding clear and shortexposition.

His main research interests are

- structured matrices: algebraic theory and fast algorithms,- interpolation problems,- operator theory and integral equations,- numerical methods for convolution equations,- applications in systems and control theory and signal processing.

In each of these topics he achieved essential contributions which is impressivelyshown by his list of publications. In my opinion, especially the importance ofhis results concerning the algebraic theory of structured matrices are strikingand imposing. In particular, in our joint paper [75] we show that inversesof matrices which are the sum of a Toeplitz and a Hankel matrix possess aBezoutian structure as inverses of Hankel or Toeplitz matrices do separately.On the basis of this structure, for example, matrix representations can befound and fast algorithms can be designed. Thus a breakthrough for the classof Toeplitz-plus-Hankel matrices was achieved.

Moreover, Georg’s observation of the kernel structure of (block) Toeplitz andToeplitz-plus-Hankel matrices turns out to be a suitable key to develop algo-rithms without additional assumptions. His ideas how to connect the struc-ture of a matrix with its additional symmetries lead to more efficient inversionand solution algorithms as well as a new kind of factorization. But also hiscontributions to Toeplitz least square problems, to transformation techniquesfor Toeplitz and Toplitz-plus-Hankel matrices leveraged the research in thesefields.

I am proud that he has completed (and still wanted to complete) many math-ematical projects with me. For many years we dreamt about writing a neattextbook on structured matrices for graduate students, ranging from the ba-sics for beginners up to recent developments. One year ago we really startedwriting the first chapters of this book. Except for some interruptions, whenwe were very busy with teaching, the collaboration was therefore especiallyintense, partly culminating in a dozen of emails per day. I received two emailsfrom him on May 10, 2005. I then did not know that they were his last!

Georg’s work leaves behind a trail that points to directions for future research.His early death leaves a loss from which we cannot recover, for it is tragic howmany plans and original ideas have passed away with him. Colleagues like meare left behind in shock and ask themselves how we can at least partially closethe gap that he has left.

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In such situations the persistent optimist Georg used to say :

“Lamenting does not help. Things are as they are.Let us confidently continue to work. This helps !”

References

[BS] Toeplitz Matrices and Singular Integral Equations: The Bernd SilbermannAnniversary Volume (Pobershau, 2001), eds. A. Bottcher, I. Gohberg,P. Junghanns, Operator Theory: Advances and Applications, Vol. 135,Birkhauser, Basel, 2002.

[SP] Problems and Methods in Mathematical Physics: The Siegfried ProssdorfMemorial Vol. (Proceed. of the 11 TMP Chemnitz, 1999), eds. J. Elschner,I. Gohberg, B. Silbermann, Operator Theory: Advances and Applications, Vol.121, Birkhauser, Basel, 2001.

[IG] The Gohberg Anniversary Collection, Vol. I (Calgary, 1988), eds. H. Dym,S. Goldberg, M.A.Kaashoek, P. Lancaster, Operator Theory: Advances andApplications, Vol. 40, Birkhauser, Basel, 1989.

List of Georg Heinig’s (refereed) publications

(chronologically ordered, including one monography [86,89], two editedproceedings [15,34], and one book translation [31])

[1] G. Heinig, K.Rost, Schur-type algorithms for the solution of HermitianToeplitz systems via factorization. Oper. Theory Adv. Appl., 160 (2005), inprint

[2] G. Codevico, G. Heinig, M. Van Barel, A superfast solver for real symmetricToeplitz systems using real trigonometric transformations. Numer. LinearAlgebra Appl., to appear.

[3] G. Heinig, K.Rost, Split algorithms for centrosymmetric Toeplitz-plus- Hankelmatrices with arbitrary rank profile. Oper. Theory Adv. Appl., to appear.

[4] T. Amdeberhan, G.Heinig, On matrices that are not similar to a Toeplitzmatrix and a family of polynomials. Linear Algebra Appl., submitted.

[5] G. Heinig, K. Rost, Fast “split” algorithms for Toeplitz and Toeplitz-plus-Hankel matrices with arbitrary rank profile. Proceedings of the InternationalConference on Mathematics and its Applications (ICMA 2004), 285–312,Kuwait, 2005.

[6] G. Heinig, K.Rost, Split algorithms for symmetric Toeplitz matrices witharbitrary rank profile. Numer. Linear Algebra Appl. 12 (2005), no. 2-3, 141–151.

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[7] G. Heinig, K. Rost, Split algorithms for Hermitian Toeplitz matrices witharbitrary rank profile. Linear Algebra Appl. 392 (2004), 235–253.

[8] G. Heinig, Fast algorithms for Toeplitz least squares problems. Current trendsin operator theory and its applications. 167–197, Oper. Theory Adv. Appl.,149, Birkhauser, Basel, 2004.

[9] G. Heinig, K. Rost, Split algorithms for skewsymmetric Toeplitz matrices witharbitrary rank profile. Theoret. Comput. Sci. 315 (2004), no. 2-3, 453–468.

[10] G. Heinig, K.Rost, New fast algorithms for Toeplitz-plus-Hankel matrices.SIAM J. Matrix Anal. Appl. 25 (2003), no. 3, 842–857.

[11] G. Heinig, K.Rost, Fast algorithms for centro-symmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices. International Conference onNumerical Algorithms, Vol. I (Marrakesh, 2001), Numer. Algorithms 33 (2003),no. 1-4, 305–317.

[12] G. Heinig, Inversion of Toeplitz-plus-Hankel matrices with arbitrary rankprofile. Fast algorithms for structured matrices: theory and applications(South Hadley, MA, 2001), 75–89, Contemp. Math., 323, Amer. Math. Soc.,Providence, RI, 2003.

[13] M.Van Barel, G. Heinig, P. Kravanja, A superfast method for solving Toeplitzlinear least squares problems. Special issue on structured matrices: analysis,algorithms and applications (Cortona, 2000), Linear Algebra Appl. 366 (2003),441–457.

[14] G. Heinig, K. Rost, Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices and Bezoutians. Special issue on structured matrices: analysis,algorithms and applications (Cortona, 2000), Linear Algebra Appl. 366 (2003),257–281.

[15] Special issue on structured matrices: analysis, algorithms and applications.Papers from the workshop held in Cortona, September 21–28, 2000. eds.D.Bini, G. Heinig, E.Tyrtyshnikov. Linear Algebra Appl. 366 (2003). ElsevierScience B.V., Amsterdam, 2003.

[16] G. Heinig, K.Rost, Fast algorithms for skewsymmetric Toeplitz matrices.Toeplitz matrices and singular integral equations (Pobershau, 2001), 193–208,Oper. Theory Adv. Appl., 135, Birkhauser, Basel, 2002.

[17] G. Heinig, On the reconstruction of Toeplitz matrix inverses from columns.Linear Algebra Appl. 350 (2002), 199–212.

[18] G. Heinig, K. Rost, Centro-symmetric and centro-skewsymmetric Toeplitzmatrices and Bezoutians. Special issue on structured and infinite systems oflinear equations. Linear Algebra Appl. 343/344 (2002), 195–209.

[19] G. Heinig, Kernel structure of Toeplitz-plus-Hankel matrices. Linear AlgebraAppl. 340 (2002), 1–13.

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[20] G. Heinig, Fast and superfast algorithms for Hankel-like matrices related toorthogonal polynomials. Numerical analysis and its applications (Rousse,2000), 385–392, Lecture Notes in Comput. Sci., 1988, Springer, Berlin, 2001.

[21] M.Van Barel, G. Heinig, P. Kravanja, An algorithm based on orthogonalpolynomial vectors for Toeplitz least squares problems. Numerical analysisand its applications (Rousse, 2000), 27–34, Lecture Notes in Comput. Sci.,1988, Springer, Berlin, 2001.

[22] M.Van Barel, G. Heinig, P. Kravanja, A stabilized superfast solver fornonsymmetric Toeplitz systems. SIAM J. Matrix Anal. Appl. 23 (2001), no.2, 494–510.

[23] G. Heinig, K. Rost, Efficient inversion formulas for Toeplitz-plus-Hankelmatrices using trigonometric transformations. Structured matrices inmathematics, computer science, and engineering, II (Boulder, CO, 1999), 247–264, Contemp. Math., 281, Amer. Math. Soc., Providence, RI, 2001.

[24] G. Heinig, Stability of Toeplitz matrix inversion formulas. Structured matricesin mathematics, computer science, and engineering, II (Boulder, CO, 1999),101–116, Contemp. Math., 281, Amer. Math. Soc., Providence, RI, 2001.

[25] G. Heinig, V. Olshevsky, The Schur algorithm for matrices with Hessenbergdisplacement structure. Structured matrices in mathematics, computerscience, and engineering, II (Boulder, CO, 1999), 3–15, Contemp. Math., 281,Amer. Math. Soc., Providence, RI, 2001.

[26] G. Heinig, Not every matrix is similar to a Toeplitz matrix. Proceedings ofthe Eighth Conference of the International Linear Algebra Society (Barcelona,1999). Linear Algebra Appl. 332/334 (2001), 519–531.

[27] G. Heinig, Chebyshev-Hankel matrices and the splitting approach for centro-symmetric Toeplitz-plus-Hankel matrices. Linear Algebra Appl. 327 (2001),no. 1-3, 181–196.

[28] S. Feldmann, G. Heinig, Partial realization for singular systems in standardform. Linear Algebra Appl. 318 (2000), no. 1-3, 127–144.

[29] G. Heinig, K.Rost, Representations of inverses of real Toeplitz-plus-Hankelmatrices using trigonometric transformations. Large-scale scientific compu-tations of engineering and environmental problems, II (Sozopol, 1999), 80–86,Notes Numer. Fluid Mech., 73, Vieweg, Braunschweig, 2000.

[30] M. Van Barel, G. Heinig, and P. Kravanja, Least squares solution of Toeplitzsystems based on orthogonal polynomial vectors. Advanced Signal ProcessingAlgorithms, Architectures, and Implementations X. ed. F.T. Luk, Vol 4116,Proceedings of SPIE (2000), 167-172.

[31] V.Maz’ya, S. Nazarov, B. Plamenevskij, Asymptotic theory of ellipticboundary value problems in singularly perturbed domains. Vol. I. Translatedfrom the German by Georg Heinig and Christian Posthoff. Operator Theory:Advances and Applications, 111. Birkhauser, Basel, 2000.

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[32] G. Heinig, K. Rost, Hartley transform representations of symmetric Toeplitzmatrix inverses with application to fast matrix-vector multiplication. SIAM J.Matrix Anal. Appl. 22 (2000), no. 1, 86–105.

[33] G. Heinig, K. Rost, Hartley transform representations of inverses of realToeplitz-plus-Hankel matrices. Proceedings of the International Conferenceon Fourier Analysis and Applications (Kuwait, 1998). Numer. Funct. Anal.Optim. 21 (2000), no. 1-2, 175–189.

[34] Proceedings of the International Conference on Fourier Analysis and Appli-cations. Held at Kuwait University, Kuwait, May 3–6, 1998. eds F. Al-Musallam, A. Bottcher, P. Butzer, G. Heinig, Vu Kim Tuan. Numer. Funct.Anal. Optim. 21 (2000), no. 1-2. Marcel Dekker, Inc., Monticello, NY, 2000.

[35] G. Heinig, F. Al-Musallam, Hermite’s formula for vector polynomial inter-polation with applications to structured matrices. Appl. Anal. 70 (1999), no.3-4, 331–345.

[36] S. Feldmann, G. Heinig, Parametrization of minimal rank block Hankel matrixextensions and minimal partial realizations. Integral Equations OperatorTheory 33 (1999), no. 2, 153–171.

[37] G. Heinig, K. Rost, DFT representations of Toeplitz-plus-Hankel Bezoutianswith application to fast matrix-vector multiplication. ILAS Symposium onFast Algorithms for Control, Signals and Image Processing (Winnipeg, MB,1997). Linear Algebra Appl. 284 (1998), no. 1-3, 157–175.

[38] G. Heinig, Matrices with higher order displacement structure. Linear AlgebraAppl. 278 (1998), no. 1-3, 295–301.

[39] G. Heinig, A.Bojanczyk, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. II. Algorithms. Linear Algebra Appl. 278 (1998), no. 1-3,11–36.

[40] G. Heinig, Properties of “derived” Hankel matrices. Recent progress inoperator theory (Regensburg, 1995), 155–170, Oper. Theory Adv. Appl., 103,Birkhauser, Basel, 1998.

[41] G. Heinig, K.Rost, Representations of Toeplitz-plus-Hankel matrices usingtrigonometric transformations with application to fast matrix-vector multi-plication. Proceedings of the Sixth Conference of the International LinearAlgebra Society (Chemnitz, 1996). Linear Algebra Appl. 275/276 (1998), 225–248.

[42] G. Heinig, F. Al-Musallam, Lagrange’s formula for tangential interpolationwith application to structured matrices. Integral Equations Operator Theory30 (1998), no. 1, 83–100.

[43] G. Heinig, Generalized Cauchy-Vandermonde matrices. Linear Algebra Appl.270 (1998), 45–77.

[44] G. Heinig, The group inverse of the transformation S(X) = 3DAX − XB.Linear Algebra Appl. 257 (1997), 321–342.

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[45] G. Heinig, A.Bojanczyk, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. I. Transformations. Proceedings of the Fifth Conferenceof the International Linear Algebra Society (Atlanta, GA, 1995). LinearAlgebra Appl. 254 (1997), 193–226.

[46] G. Heinig, L.A. Sakhnovich, I. F. Tidniuk, Paired Cauchy matrices. LinearAlgebra Appl. 251 (1997), 189–214.

[47] G. Heinig, Solving Toeplitz systems after extension and transformation.Toeplitz matrices: structures, algorithms and applications (Cortona, 1996).Calcolo 33 (1998), no. 1-2, 115–129.

[48] S. Feldmann, G. Heinig, On the partial realization problem for singularsystems. Proceedings of the 27th Annual Iranian Mathematics Conference(Shiraz, 1996), 79–100, Shiraz Univ., Shiraz, 1996.

[49] S. Feldmann, G. Heinig, Vandermonde factorization and canonical represen-tations of block Hankel matrices. Proceedings of the Fourth Conference ofthe International Linear Algebra Society (ILAS) (Rotterdam, 1994). LinearAlgebra Appl. 241/243 (1996), 247–278.

[50] G. Heinig, Inversion of generalized Cauchy matrices and other classes ofstructured matrices. Linear algebra for signal processing (Minneapolis, MN,1992), 63–81, IMA Vol. Math. Appl., 69, Springer, New York, 1995.

[51] G. Heinig, Matrix representations of Bezoutians. Special issue honoringMiroslav Fiedler and Vlastimil Ptak. Linear Algebra Appl. 223/224 (1995),337–354.

[52] G. Heinig, K.Rost, Recursive solution of Cauchy-Vandermonde systems ofequations. Linear Algebra Appl. 218 (1995), 59–72.

[53] G. Heinig, Generalized inverses of Hankel and Toeplitz mosaic matrices. LinearAlgebra Appl. 216 (1995), 43–59.

[54] G. Heinig, F. Hellinger, Displacement structure of generalized inverse matrices.Generalized inverses (1993). Linear Algebra Appl. 211 (1994), 67–83.

[55] G. Heinig, F. Hellinger, The finite section method for Moore-Penrose inversionof Toeplitz operators. Integral Equations Operator Theory 19 (1994), no. 4,419–446.

[56] G. Heinig, F. Hellinger, Displacement structure of pseudoinverses. SecondConference of the International Linear Algebra Society (ILAS) (Lisbon, 1992).Linear Algebra Appl. 197/198 (1994), 623–649.

[57] S. Feldmann, G. Heinig, Uniqueness properties of minimal partial realizations.Linear Algebra Appl. 203/204 (1994), 401–427.

[58] G. Heinig, F. Hellinger, Moore-Penrose inversion of square Toeplitz matrices.SIAM J. Matrix Anal. Appl. 15 (1994), no. 2, 418–450.

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[59] A.W. Bojanczyk, G. Heinig, A multi-step algorithm for Hankel matrices. J.Complexity 10 (1994), no. 1, 142–164.

[60] G. Heinig, F. Hellinger, On the Bezoutian structure of the Moore-Penroseinverses of Hankel matrices. SIAM J. Matrix Anal. Appl. 14 (1993), no. 3,629–645.

[61] T. Finck, G. Heinig, K. Rost, An inversion formula and fast algorithms forCauchy-Vandermonde matrices. Linear Algebra Appl. 183 (1993), 179–191.

[62] G. Heinig, P. Jankowski, Kernel structure of block Hankel and Toeplitzmatrices and partial realization. Linear Algebra Appl. 175 (1992), 1–30.

[63] G. Heinig, Inverse problems for Hankel and Toeplitz matrices. Linear AlgebraAppl. 165 (1992), 1–23.

[64] G. Heinig, Fast algorithms for structured matrices and interpolation problems.Algebraic computing in control (Paris, 1991), 200–211, Lecture Notes inControl and Inform. Sci., 165, Springer, Berlin, 1991.

[65] G. Heinig, On structured matrices, generalized Bezoutians and generalizedChristoffel-Darboux formulas. Topics in matrix and operator theory(Rotterdam, 1989), 267–281, Oper. Theory Adv. Appl., 50, Birkhauser, Basel,1991.

[66] G. Heinig, Formulas and algorithms for block Hankel matrix inversion andpartial realization. Signal processing, scattering and operator theory, andnumerical methods (Amsterdam, 1989), 79–90, Progr. Systems ControlTheory, 5, Birkhauser Boston, Boston, MA, 1990.

[67] G. Heinig, P. Jankowski, Parallel and superfast algorithms for Hankel systemsof equations. Numer. Math. 58 (1990), no. 1, 109–127.

[68] G. Heinig, P. Jankowski, Fast algorithms for the solution of general Toeplitzsystems. Wiss. Z. Tech. Univ. Karl-Marx-Stadt 32 (1990), no. 1, 12–17.

[69] G. Heinig, K.Rost, Matrices with displacement structure, generalized Be-zoutians, and Moebius transformations. The Gohberg anniversary collection,Vol. I (Calgary, AB, 1988), 203–230, Oper. Theory Adv. Appl., 40, Birkhauser,Basel, 1989.

[70] G. Heinig, K.Rost, Inversion of matrices with displacement structure. IntegralEquations Operator Theory 12 (1989), no. 6, 813–834.

[71] G. Heinig, W. Hoppe, K.Rost, Structured matrices in interpolation andapproximation problems. Wiss. Z. Tech. Univ. Karl-Marx-Stadt 31 (1989),no. 2, 196–202.

[72] G. Heinig, K.Rost, Matrix representations of Toeplitz-plus-Hankel matrixinverses. Linear Algebra Appl. 113 (1989), 65–78.

[73] G. Heinig, T. Amdeberhan, On the inverses of Hankel and Toeplitz mosaicmatrices. Seminar Analysis (Berlin, 1987/1988), 53–65, Akademie-Verlag,Berlin, 1988.

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[74] G. Heinig, P. Jankowski, K. Rost, Tikhonov regularisation for block Toeplitzmatrices. Wiss. Z. Tech. Univ. Karl-Marx-Stadt 30 (1988), no. 1, 41–45.

[75] G. Heinig, K.Rost, On the inverses of Toeplitz-plus-Hankel matrices. LinearAlgebra Appl. 106 (1988), 39–52.

[76] G. Heinig, P. Jankowski, K. Rost, Fast inversion algorithms of Toeplitz-plus-Hankel matrices. Numer. Math. 52 (1988), no. 6, 665–682.

[77] G. Heinig, Structure theory and fast inversion of Hankel striped matrices. I.Integral Equations Operator Theory 11 (1988), no. 2, 205–229.

[78] G. Heinig, K. Rost, Inversion of generalized Toeplitz-plus-Hankel matrices.Wiss. Z. Tech. Univ. Karl-Marx-Stadt 29 (1987), no. 2, 209–211.

[79] G. Heinig, U. Jungnickel, Hankel matrices generated by Markov parameters,Hankel matrix extension, partial realization, and Pade-approximation.Operator theory and systems (Amsterdam, 1985), 231–253, Oper. Theory Adv.Appl., 19, Birkhauser, Basel, 1986.

[80] G. Heinig, U. Jungnickel, Lyapunov equations for companion matrices. LinearAlgebra Appl. 76 (1986), 137–147.

[81] G. Heinig, U. Jungnickel, Hankel matrices generated by the Markov parametersof rational functions. Linear Algebra Appl. 76 (1986), 121–135.

[82] G. Heinig, Partial indices for Toeplitz-like operators. Integral EquationsOperator Theory 8 (1985), no. 6, 805–824.

[83] G. Heinig, K.Rost, Fast inversion of Toeplitz-plus-Hankel matrices. Wiss. Z.Tech. Hochsch. Karl-Marx-Stadt 27 (1985), no. 1, 66–71.

[84] G. Heinig, U. Jungnickel, On the Bezoutian and root localization for poly-nomials. Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 27 (1985), no. 1, 62–65.

[85] G. Heinig, B. Silbermann, Factorization of matrix functions in algebrasof bounded functions. Spectral theory of linear operators and relatedtopics (Timisoara/Herculane, 1983), 157–177, Oper. Theory Adv. Appl., 14,Birkhauser, Basel, 1984.

[86] G. Heinig, K. Rost, Algebraic methods for Toeplitz-like matrices and operators.Oper. Theory Adv. Appl., 13, Birkhauser, Basel, 1984.

[87] G. Heinig, U. Jungnickel, On the Routh-Hurwitz and Schur-Cohn problemsfor matrix polynomials and generalized Bezoutians. Math. Nachr. 116 (1984),185–196.

[88] G. Heinig, K.Rost, Schnelle Invertierungsalgorithmen fur einige Klassen vonMatrizen. (German) [Fast inversion algorithms for some classes of matrices]Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 26 (1984), no. 2, 235–241.

[89] G. Heinig, K. Rost, Algebraic methods for Toeplitz-like matrices and operators.Mathematical Research, 19, Akademie-Verlag, Berlin, 1984.

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[90] G. Heinig, K.Rost, Invertierung von Toeplitzmatrizen und ihren Verallge-meinerungen. I. Die Methode der UV -Reduktion. (German) [Inversion ofToeplitz matrices and their generalizations. I. The method of UV -reduction]Beitrage Numer. Math. No. 12 (1984), 55–73.

[91] G. Heinig, Generalized resultant operators and classification of linear operatorpencils up to strong equivalence. Functions, series, operators, Vol. I, II(Budapest, 1980), 611–620, Colloq. Math. Soc. Janos Bolyai, 35, North-Holland, Amsterdam, 1983.

[92] G. Heinig, Inversion of Toeplitz and Hankel matrices with singular sections.Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 25 (1983), no. 3, 326–333.

[93] G. Heinig, U. Jungnickel, Zur Losung von Matrixgleichungen der Form AX −

XB = 3DC. (German) [On the solution of matrix equations of the formAX − XB = 3DC] Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 23 (1981), no.4, 387–393.

[94] G. Heinig, Linearisierung und Realisierung holomorpher Operatorfunktionen.(German) Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 22 (1980), no. 5, 453–459.

[95] G. Heinig, K.Rost, Invertierung einiger Klassen von Matrizen und Ope-ratoren. I. Endliche Toeplitzmatrizen und ihre Verallgemeinerungen. (Ger-man) [Inversion of some classes of matrices and operators. I. FiniteToeplitz matrices and their generalizations] Wissenschaftliche Informationen[Scientific Information], 12, Technische Hochschule Karl-Marx-Stadt, SektionMathematik, Karl-Marx-Stadt, 1979.

[96] G. Heinig, Bezoutiante, Resultante und Spektralverteilungsprobleme furOperatorpolynome. (German) Math. Nachr. 91 (1979), 23–43.

[97] G. Heinig, Transformationen von Toeplitz- und Hankelmatrizen. (German)Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 21 (1979), no. 7, 859–864.

[98] G. Heinig, Invertibility of singular integral operators. (Russian) Soobshch.Akad. Nauk Gruzin. SSR 96 (1979), no. 1, 29–32.

[99] G. Heinig, Uber ein kontinuierliches Analogon der Begleitmatrix eines Poly-noms und die Linearisierung einiger Klassen holomorpher Operatorfunktionen.(German) Beitrage Anal. 13 (1979), 111–126.

[100] G. Heinig, Verallgemeinerte Resultantenbegriffe bei beliebigen Matrixbuscheln.II. Gemischter Resultantenoperator. (German) Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 20 (1978), no. 6, 701–703.

[101] G. Heinig, Verallgemeinerte Resultantenbegriffe bei beliebigen Matrixbuscheln.I. Einseitiger Resultantenoperator. (German) Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 20 (1978), no. 6, 693–700.

[102] G. Heinig, Endliche Toeplitzmatrizen und zweidimensionale Wiener-Hopf-Operatoren mit homogenem Symbol. II. Uber die normale Auflosbarkeit einerKlasse zweidimensionaler Wiener-Hopf Operatoren. (German) Math. Nachr.82 (1978), 53–68.

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[103] G. Heinig, Endliche Toeplitzmatrizen und zweidimensionale Wiener-Hopf-Operatoren mit homogenem Symbol. I. Eigenschaften endlicher Toeplitzma-trizen. (German) Math. Nachr. 82 (1978), 29–52.

[104] G. Heinig, K. Rost, Uber homogene Gleichungen vom Faltungstyp auf einemendlichen Intervall. (German) Demonstratio Math. 10 (1977), no. 3-4, 791–806.

[105] G. Heinig, Uber Block-Hankelmatrizen und den Begriff der Resultante furMatrixpolynome. (German) Wiss. Z. Techn. Hochsch. Karl-Marx-Stadt 19(1977), no. 4, 513–519.

[106] G. Heinig, The notion of Bezoutian and of resultant for operator pencils.(Russian) Funkcional. Anal. i Prilozen. 11 (1977), no. 3, 94–95.

[107] I. C. Gohberg, G. Heinig, The resultant matrix and its generalizations. II. Thecontinual analogue of the resultant operator. (Russian) Acta Math. Acad. Sci.Hungar. 28 (1976), no. 3-4, 189–209.

[108] G. Heinig, Periodische Jacobimatrizen im entarteten Fall. (German) Wiss. Z.Techn. Hochsch. Karl-Marx-Stadt 18 (1976), no. 4, 419–423.

[109] G. Heinig, Uber die Invertierung und das Spektrum von singularen Integral-operatoren mit Matrixkoeffizienten. (German) 5. Tagung uber Probleme undMethoden der Mathematischen Physik (Techn. Hochschule Karl-Marx-Stadt,Karl-Marx-Stadt, 1975), Heft 1, 52–59. Wiss. Schr. Techn. Hochsch. Karl-Marx-Stadt, Techn. Hochsch., Karl-Marx-Stadt, 1975.

[110] I. C. Gohberg, G. Heinig, On matrix integral operators on a finite intervalwith kernels depending on the difference of the arguments. (Russian) Rev.Roumaine Math. Pures Appl. 20 (1975), 55–73.

[111] I. C. Gohberg, G. Heinig, The resultant matrix and its generalizations. I. Theresultant operator for matrix polynomials. (Russian) Acta Sci. Math. (Szeged)37 (1975), 41–61.

[112] I. C. Gohberg, G. Heinig, Inversion of finite Toeplitz matrices consisting ofelements of a noncommutative algebra. (Russian) Rev. Roumaine Math. PuresAppl. 19 (1974), 623–663.

[113] G. Heinig, The inversion and the spectrum of matrix Wiener-Hopf operators.(Russian) Mat. Sb. (N.S.) 91(133) (1973), 253–266.

[114] G. Heinig, The inversion and the spectrum of matrix-valued singular integraloperators. (Russian) Mat. Issled. 8 (1973), no. 3(29), 106–121.

[115] I. C. Gohberg, G. Heinig, The inversion of finite Toeplitz matrices. (Russian)Mat. Issled. 8 (1973), no. 3(29), 151–156.

[116] G. Heinig, Inversion of periodic Jacobi matrices. (Russian) Mat. Issled. 8(1973), no. 1(27), 180–200.

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