Numerical Linear Algebra

An Introduction

AvHolger Wendland

Inbunden, Engelska, 2017

Del 56 i serien Cambridge Texts in Applied Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2017-11-16
Mått:157 x 235 x 28 mm
Vikt:710 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Texts in Applied Mathematics
Antal sidor:418
Förlag:Cambridge University Press
ISBN:9781107147133

Utforska kategorier

Teknik: allmänt inom Naturvetenskap och teknik
Informationsteknik: allmänt inom Data och IT
Algebra inom Naturvetenskap och teknik

Mer om författaren

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).

Recensioner i media

'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

Innehållsförteckning

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.