Numerical Linear Algebra: An Introduction

by Holger Wendland

Overview

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

Product Details

ISBN-13:	9781316601174
Publisher:	Cambridge University Press
Publication date:	11/16/2017
Series:	Cambridge Texts in Applied Mathematics , #56
Pages:	418
Product dimensions:	5.98(w) x 8.94(h) x 0.98(d)

About the Author

Holger Wendland holds the Chair of Applied and Numerical Analysis at the Universität Bayreuth, Germany. He works in the area of Numerical Analysis and is the author of two books, Scattered Data Approximation (Cambridge, 2005) and Numerische Mathematik (2004, with Robert Schaback).

Table of Contents

Part I. Preliminaries: 1. Introduction; 2. Error, stability and conditioning; Part II. Basic Methods: 3. Direct methods for solving linear systems; 4. Iterative methods for solving linear systems; 5. Calculation of eigenvalues; Part III. Advanced Methods: 6. Methods for large sparse systems; 7. Methods for large dense systems; 8. Preconditioning; 9. Compressed sensing; References; Index.

Editorial Reviews

'Wendland delivers an introductory textbook on numerical linear algebra intended for advanced undergraduate and graduate students in applied mathematics. The book covers fairly standard material in this area; it includes error analysis and ill-conditioning, direct and iterative methods for the solution of linear systems of equations, least squares problems, and eigenvalue problems. Additional advanced topics that are not usually covered in introductory textbooks include multipole expansions, domain decomposition methods, and compressive sensing. The book is generally theoretical and mathematically rigorous in its approach. Algorithms are given only in pseudocode. … The text will be of interest primarily to instructors and students in graduate numerical linear algebra courses.' B. Borchers, Choice

'Wendland’s book provides the reader with rigorous and clean proofs throughout the text. There are a lot of new concepts being presented that can spark the interest of a student who wishes to take numerical linear algebra and can also serve as an excellent resource for an independent study. If you are considering a new text for your numerical linear algebra class or wish to supplement with another resource, I would recommend giving this book a review.' Peter Olszewski, MAA Reviews

From the Publisher