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