Theoretical numerical analysis: A functional analysis framework

Weimin Han, Kendall E. Atkinson (auth.)9781441904577, 1441904573

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, boundary integral equations for planar regions, and multivariable polynomial approximations. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. In this third edition, a new chapter, Multivariable Polynomial Approximations, is included, numerous changes are made throughout the entire text, and new exercises are added.

Review of earlier edition:

“…the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references.”

R. Glowinski, SIAM Review, 2003

Table of contents :
Front Matter….Pages 1-13
Linear Spaces….Pages 1-50
Linear Operators on Normed Spaces….Pages 51-113
Approximation Theory….Pages 115-166
Fourier Analysis and Wavelets….Pages 167-206
Nonlinear Equations and Their Solution by Iteration….Pages 207-252
Finite Difference Method….Pages 253-275
Sobolev Spaces….Pages 277-326
Weak Formulations of Elliptic Boundary Value Problems….Pages 327-365
The Galerkin Method and Its Variants….Pages 367-382
Finite Element Analysis….Pages 383-422
Elliptic Variational Inequalities and Their Numerical Approximations….Pages 423-471
Numerical Solution of Fredholm Integral Equations of the Second Kind….Pages 473-549
Boundary Integral Equations….Pages 551-581
Multivariable Polynomial Approximations….Pages 583-599
Back Matter….Pages 1-24