Overview
- Is the first book to provide details on the COCR, BiCR, and GPBiCG methods to solve non-Hermitian linear systems
- Describes theoretical applications to solve problems such as shifted linear systems and matrix functions
- Shows practical applications, as in partial differential equations, computational physics, and (Riemannian) optimization
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 60)
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Table of contents (5 chapters)
Keywords
About this book
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.
Authors and Affiliations
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Bibliographic Information
Book Title: Krylov Subspace Methods for Linear Systems
Book Subtitle: Principles of Algorithms
Authors: Tomohiro Sogabe
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-981-19-8532-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
Hardcover ISBN: 978-981-19-8531-7Published: 21 January 2023
Softcover ISBN: 978-981-19-8534-8Published: 21 January 2024
eBook ISBN: 978-981-19-8532-4Published: 20 January 2023
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: XIII, 225
Number of Illustrations: 20 b/w illustrations
Topics: Numerical Analysis, Mathematical Modeling and Industrial Mathematics, Algorithms