Krylov subspace methods for linear systems : principles of algorithms / Tomohiro Sogabe.
Sogabe, Tomohiro.
2022
QA402
Available Online

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Title Krylov subspace methods for linear systems : principles of algorithms / Tomohiro Sogabe.
Author Sogabe, Tomohiro.
ISBN 9789811985324 (electronic bk.)
9811985324 (electronic bk.)
9811985316
9789811985317
DOI https://doi.org/10.1007/978-981-19-8532-4
Published Singapore : Springer, 2022.
Language English
Description 1 online resource (216 pages) : illustrations (black and white).
Item Number 10.1007/978-981-19-8532-4 doi
Call Number QA402
Dewey Decimal Classification 003/.74
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Springer series in computational mathematics ; v. 60.
Available in Other Form KRYLOV SUBSPACE METHODS FOR LINEAR SYSTEMS.
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All Resources
Introduction to Numerical Methods for Solving Linear Systems
Some Applications to Computational Science and Data Science
Classication and Theory of Krylov Subspace Methods
Applications to Shifted Linear Systems
Applications to Matrix Functions.

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