Theoretical Numerical Analysis: A Functional Analysis Framework (Texts in Applied Mathematics) by Kendall Atkinson

by Kendall E. Atkinson

The book presents an abstract point of view of Numerical Analysis (as one can immediatly see by the title!). It is written by a master in the topic, author of more than 70 publications at the higher levels, well known for his contributions in Integral and Partial Differential Equations. If one is interested on the basic aspects of numerical analysis, I also suggest to consider his well known manual "Elementary Numerical Analysis".The present book presents several aspects that are not covered by most of the manuals in Numerical Analysis and highly contributes to have a wider idea of convergence and stability of some well known methods.

Genres: Mathematics

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.