Term ProjectTerm Project

Applications of Computer Programming in Earth Sciences

Instructor: Dr. Cheng-Chien Liu

Department of Earth Sciences

National Cheng Kung University

Last updated: April 21, 2023

ChapterChapter

Project descriptionProject description

Solution of Linear Algebraic Equations Solution of Linear Algebraic Equations • Gauss-Jordan matrix inversion and linear equation

solution (2.1)• Linear equation solution, backsubstitution (2.3)（駱守凡）

• Singular value decomposition of a matrix (2.6) Interpolation and Extrapolation Interpolation and Extrapolation • Two-dimensional polynomial interpolation (3.6)（張家鳳）

• Two-dimensional bicubic interpolation (3.6)（劉益廷）

• Two-dimensional spline interpolation (3.6)

Project description (cont.)Project description (cont.)

Integration of FunctionsIntegration of Functions• Integrate a function over a three-dimensional space

(4.6) （林維芝） Evaluation of FunctionsEvaluation of Functions• Evaluate a polynomial and its derivatives (5.3) （李涵瑜）

Random NumbersRandom Numbers• Random deviates from DES-like hashing (7.5)（蘇鴻林）

• Adaptive multidimensional Monte Carlo integration (7.8) （王博賢）

Project description (cont.)Project description (cont.)

SortingSorting• Sort an array by quicksort method (8.2) （王若梅）• Find the Nth largest, without altering an array (8.5)（盧旭宇）

• Find M largest values, without altering an array (8.5)（黃姿勳）

Root Finding and Nonlinear Sets of EquationsRoot Finding and Nonlinear Sets of Equations• Find root of a function by Ridders‘ method (9.2) （劉晃丞）• Find root of a function by Brent's method (9.3) （歐兆強）• Find root of a function by Newton-Raphson and bisection (9.4) （陳治宇）

• roots of a polynomial by Laguerre's method with deflation (9.5) （蕭雅竹）

Project description (cont.)Project description (cont.)

Eigensystems Eigensystems • Eigenvalues and eigenvectors of a symmetric matrix

(11.1) (李奇峰 ) Fast Fourier Transform Fast Fourier Transform • Fast Fourier transform in multidimensions (12.4)

(江彥廷 ) Fourier and Spectral Applications Fourier and Spectral Applications • Correlation or autocorrelation of data using FFT

(13.2) (唐健庭 ) Modeling of Data Modeling of Data • Fit a polynomial using LFIT or SVDFIT (15.4)