Numerical Methods

I. FUNDAMENTAL CONCEPTS - Algorithms and Error Propagation / Matrices / II. LINEAR EQUATIONS AND INEQUALITIES - Gaussian Elimination / The LU Factorization / The Exchange Algorithm / The Cholesky Factorizaton / The QU Factorization / Relaxation Methods / Data Fitting / Linear Optimization / III. ITERATION - Vector Iteration / The KR Algorithm / One-Dimensional Iteration / Multi-dimensional Iteration / Roots of Polynomials / Bernoulli's Method / The QD Algorithm / IV. INTERPOLATION AND DISCRETE APPROXIMATION - Interpolation / Discrete Approximation / Polynomials in Bezier Form / Splines / V. NUMERICAL DIFFERENTIATION AND INTEGRATION - Numericals Differentiation and Integration / Extrapolation / One-Step Methods for Differential Equations / Linear Multi-Step Methods for Differential Equations / The Methods by Ritz And Galerkin / The Finite Element Method / Bibliography / Index

The development and analysis of constructive algorithms in Numerical Mathematics has become a focus of applied mathematics since the practical realization of these algorithms by electronic computers is no longer restricted to trivial examples. This book describes algorithmic solutions whose basic ideas are common to a variety of mathematical problems. By means of the methods presented, the reader will acquire the skills besides a fundamental knowledge to successfully work on related subjects in this field.