Numerical Linear Algebra

An Introduction

Holger Wendland (Universität Bayreuth, Germany)

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English

Cambridge University Press
16 November 2017

Algebra; Numerical analysis; Maths for engineers

Series: Cambridge Texts in Applied Mathematics

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.

By: Holger Wendland (Universität Bayreuth Germany)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 56
Dimensions: Height: 235mm, Width: 157mm, Spine: 28mm
Weight: 710g
ISBN: 9781107147133
ISBN 10: 1107147131
Series: Cambridge Texts in Applied Mathematics
Pages: 418
Publication Date: 16 November 2017
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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).

Reviews for Numerical Linear Algebra: An Introduction

'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 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