Krylov Subspace Methods For Linear Systems

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Krylov Subspace Methods For Linear Systems

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Author : Tomohiro Sogabe
language : en
Publisher: Springer Nature
Release Date : 2023-01-20

Krylov Subspace Methods For Linear Systems written by Tomohiro Sogabe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Mathematics categories.

This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.

Inexact Krylov Subspace Methods For Linear Systems

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Author : Gerard L. G. Sleijpen
language : en
Publisher:
Release Date : 2002

Inexact Krylov Subspace Methods For Linear Systems written by Gerard L. G. Sleijpen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.

Krylov Methods For Nonsymmetric Linear Systems

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Author : Gérard Meurant
language : en
Publisher: Springer Nature
Release Date : 2020-10-02

Krylov Methods For Nonsymmetric Linear Systems written by Gérard Meurant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.

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.

Preconditioned Krylov Subspace Methods For Linear Systems

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Author : Noriko Hosoi
language : en
Publisher:
Release Date : 1993

Preconditioned Krylov Subspace Methods For Linear Systems written by Noriko Hosoi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Linear systems categories.

Krylov Subspace Methods For Large Linear Systems Of Equations

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Author : G. L. G. Sleijpen
language : en
Publisher:
Release Date : 1993

Krylov Subspace Methods For Large Linear Systems Of Equations written by G. L. G. Sleijpen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Krylov Subspace Methods

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Author : Jörg Liesen
language : en
Publisher: Numerical Mathematics and Scie
Release Date : 2013

Krylov Subspace Methods written by Jörg Liesen and has been published by Numerical Mathematics and Scie this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.

Krylov Subspace Methods For Solving Large Unsymmetric Linear Systems

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Author : Y. Saad
language : en
Publisher:
Release Date : 1981

Krylov Subspace Methods For Solving Large Unsymmetric Linear Systems written by Y. Saad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Conjugate gradient methods categories.

Krylov Subspace Methods For Linear Systems Eigenvalues And Model Order Reduction

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Author : Daniel Skoogh
language : en
Publisher:
Release Date : 1998

Krylov Subspace Methods For Linear Systems Eigenvalues And Model Order Reduction written by Daniel Skoogh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Optimizing Krylov Subspace Methods For Linear Systems And Least Squares Problems

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Author : Mei Yang (Ph.D.)
language : en
Publisher:
Release Date : 2019

Optimizing Krylov Subspace Methods For Linear Systems And Least Squares Problems written by Mei Yang (Ph.D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Generalized minimal residual method categories.

Mixed Product Krylov Subspace Methods For Solving Nonsymmetric Linear Systems

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Author : Tracy L. Ewen
language : en
Publisher:
Release Date : 2000

Mixed Product Krylov Subspace Methods For Solving Nonsymmetric Linear Systems written by Tracy L. Ewen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.