Applied numerical methods using MATLAB / Won Young Yang ... [et al.].

Includes bibliographical references (p. 497-498) and indexes.

APPLIED NUMERICAL METHODS USING MATLAB®; CONTENTS; Preface; 1 MATLAB Usage and Computational Errors; 1.1 Basic Operations of MATLAB; 1.1.1 Input/Output of Data from MATLAB Command Window; 1.1.2 Input/Output of Data Through Files; 1.1.3 Input/Output of Data Using Keyboard; 1.1.4 2-D Graphic Input/Output; 1.1.5 3-D Graphic Output; 1.1.6 Mathematical Functions; 1.1.7 Operations on Vectors and Matrices; 1.1.8 Random Number Generators; 1.1.9 Flow Control; 1.2 Computer Errors Versus Human Mistakes; 1.2.1 IEEE 64-bit Floating-Point Number Representation; 1.2.2 Various Kinds of Computing Errors 1.2.3 Absolute/Relative Computing Errors1.2.4 Error Propagation; 1.2.5 Tips for Avoiding Large Errors; 1.3 Toward Good Program; 1.3.1 Nested Computing for Computational Efficiency; 1.3.2 Vector Operation Versus Loop Iteration; 1.3.3 Iterative Routine Versus Nested Routine; 1.3.4 To Avoid Runtime Error; 1.3.5 Parameter Sharing via Global Variables; 1.3.6 Parameter Passing Through Varargin; 1.3.7 Adaptive Input Argument List; Problems; 2 System of Linear Equations; 2.1 Solution for a System of Linear Equations; 2.1.1 The Nonsingular Case (M = N) 2.1.2 The Underdetermined Case (M N): Least-Squares Error Solution; 2.1.4 RLSE (Recursive Least-Squares Estimation); 2.2 Solving a System of Linear Equations; 2.2.1 Gauss Elimination; 2.2.2 Partial Pivoting; 2.2.3 Gauss-Jordan Elimination; 2.3 Inverse Matrix; 2.4 Decomposition (Factorization); 2.4.1 LU Decomposition (Factorization): Triangularization; 2.4.2 Other Decomposition (Factorization): Cholesky, QR, and SVD; 2.5 Iterative Methods to Solve Equations; 2.5.1 Jacobi Iteration; 2.5.2 Gauss-Seidel Iteration 2.5.3 The Convergence of Jacobi and Gauss-Seidel IterationsProblems; 3 Interpolation and Curve Fitting; 3.1 Interpolation by Lagrange Polynomial; 3.2 Interpolation by Newton Polynomial; 3.3 Approximation by Chebyshev Polynomial; 3.4 Pade Approximation by Rational Function; 3.5 Interpolation by Cubic Spline; 3.6 Hermite Interpolating Polynomial; 3.7 Two-dimensional Interpolation; 3.8 Curve Fitting; 3.8.1 Straight Line Fit: A Polynomial Function of First Degree; 3.8.2 Polynomial Curve Fit: A Polynomial Function of Higher Degree; 3.8.3 Exponential Curve Fit and Other Functions 3.9 Fourier Transform3.9.1 FFT Versus DFT; 3.9.2 Physical Meaning of DFT; 3.9.3 Interpolation by Using DFS; Problems; 4 Nonlinear Equations; 4.1 Iterative Method Toward Fixed Point; 4.2 Bisection Method; 4.3 False Position or Regula Falsi Method; 4.4 Newton( -Raphson) Method; 4.5 Secant Method; 4.6 Newton Method for a System of Nonlinear Equations; 4.7 Symbolic Solution for Equations; 4.8 A Real-World Problem; Problems; 5 Numerical Differentiation/Integration; 5.1 Difference Approximation for First Derivative; 5.2 Approximation Error of First Derivative