Theoretical Numerical Analysis: A Functional Analysis Framework

by Kendall E. Atkinson, Weimin Han

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, and boundary integral equations for planar regions. 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. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added. Review of earlier "...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

Genres: Mathematics

641 pages, Hardcover

First published November 6, 2004

Reviews

[Ayush Vatsa · Rating 4 out of 5]

A rigorous exploration of numerical methods, emphasizing Banach and Hilbert space frameworks. the book provides far better insights into operator approximations, stability through coercivity, and spectral analysis of discretization errors it examines projection techniques such as Galerkin methods and iterative solvers like GMRES within an abstract functional setting. Only drawback or maybe advantage based on who's going to read this is it requires reader with a strong foundation in functional analysis and operator theory, because the book is rather abstract and dense. (Like a good maths book should be, less wordcelling)

[HikBook]

Good book! Sobolev periodic spaces and poisson equation

[Nguyễn Năng · Rating 2 out of 5]

So far, the book is rather hard to read because of its monotonous word-by-word structure. For a study of mathematical structures (functional analysis), this book can use a lot of emphasizing boxes, bold phrases, and separated blocks to highlight key concepts and results.