Theoretical Numerical Analysis: A Functional Analysis Framework

by Kendall E. Atkinson, Weimin Han

This textbook covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis. For this second edition, a new chapter on Fourier analysis and wavelets and over 140 new exercises have been added, almost doubling the exercise amount from the last edition. Many sections from the first edition have been revised. Some of the other topics covered in this book are functional analysis and approximation theory, nonlinear analysis, Sobolev spaces, elliptic boundary value problems and variational inequalities.

Genres: Mathematics

576 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.