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Springer Series in Computational Mathematics

Krylov Methods for Nonsymmetric Linear Systems

From Theory to Computations

Authors: Meurant, Gérard, Duintjer Tebbens, Jurjen

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  • Contains an overview of state-of-the-art Krylov subspace methods including new theoretical convergence results
  • Emphasis is placed on the construction of examples with prescribed convergence histories for many of the described methods
  • Matlab codes included for most of the described methods and techniques
  • New results are presented in the context of a unifying framework that are valid for classes of methods (so-called quasi-minimum residual and quasi-orthogonal residual methods)
  • Contains descriptions of important methods not treated in previous books 
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eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-030-55251-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
About this book

This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties.  Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods.
This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.

Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-030-55251-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Krylov Methods for Nonsymmetric Linear Systems
Book Subtitle
From Theory to Computations
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
57
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-55251-0
DOI
10.1007/978-3-030-55251-0
Hardcover ISBN
978-3-030-55250-3
Series ISSN
0179-3632
Edition Number
1
Number of Pages
XIV, 686
Number of Illustrations
184 b/w illustrations
Topics