Theoretical Numerical Analysis: A Functional Analysis Framework

by Kendall E. Atkinson, Weimin Han

This text gives an introduction to functional analysis for graduate students pursuing research involving numerical analysis. The text covers basic results of functional analysis as well as additional topics needed in theoretical numerical analysis. Applications of this functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. Extensive exercises are included at the end of each section along with recommendations for additional reading. This book is especially suited to students interested in the numerical solution of differential and/or integral equations, but it should appeal to numerical analysts and mathematically-oriented students and researchers in engineering, physics, and related areas.

Genres: Mathematics

472 pages, Hardcover

First published January 1, 2001

Reviews

[Ayush Vatsa]

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]

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.