Introduction to Numerical ComputationAnalysis and Matlab illustrations

Introduction to Numerical ComputationAnalysis and Matlab illustrations

This ebook contains the following topics: Mathematical Models and Numerical Approximations, Numerical Computation, References, Sources of Error, Basic Concepts, Error Propagation, Number Representation, Rounding Errors in Floating Point, Arithmetic Operations in Floating Point, Accumulated Errors, IEEE Standard, Introduction, Remainder Term Estimates, Standard Functions, Range Reduction, Trigonometric Functions, Introduction, Crude Localization, Iteration Methods, Convergence Analysis, Error Estimation and StoppingCriteria, Algebraic Equations, Square Root, Nonlinear Systems, Introduction, Interpolation by Polynomials, Linear Interpolation, Lagrange Interpolation, Hermite Interpolation, Splines, Linear Spline Functions, Cubic Splines, Introduction, Richardson Extrapolation, Introduction, Trapezoidal Rule, Adaptive Quadrature, Introduction, Triangular Systems, Gaussian Elimination, Pivoting, LU Factorization, Band Matrices, Inverse Matrix, Vector and Matrix Norms, Sensitivity Analysis, Rounding Errors, Estimation of Condition Number, Overdetermined Systems, QR Factorization, Introduction, Important Concepts, Least Squares Method, Orthogonal Functions, Orthogonal Polynomials, Legendre Polynomials, Chebyshev Polynomials, Discrete Cosine Transform, Minimax Approximation, Introduction, Initial Value Problems, Local and Global Error, An Implicit Method, Stability, Adaptive Step Length Control, Boundary Value Problems, A Finite Element Method, The Shooting Method, Mathematical Models and Numerical Approximations

Author(s): Lars Elden Linde Wittmeyer-Koch Hans Bruun Nielsen

383 Pages