Krylov Subspace Methods for Linear Systems

Principles of Algorithms

Tomohiro Sogabe (Autor)

Buch | Hardcover

225 Seiten

2023 | 1st ed. 2022
Springer Verlag, Singapore
978-981-19-8531-7 (ISBN)

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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.

He is an associate professor at the department of Applied Physics, Nagoya University, Japan. His research interests include numerical linear algebra, numerical multilinear algebra, and scientific computing. He published over 70 research articles and is best known for extensions of the Conjugate Residual method: the BiCR method and the COCR method for large and sparse linear systems. He serves as an editor of Japan Journal of Industrial and Applied Mathematics, Springer, since 2019. He is a member of the board of directors of Japan SIAM since 2021.

Introduction to Numerical Methods for Solving Linear Systems.- Some Applications to Computational Science and Data Science.- Classiﬁcation and Theory of Krylov Subspace Methods.- Applications to Shifted Linear Systems.- Applications to Matrix Functions.

Erscheinungsdatum	25.01.2023
Reihe/Serie	Springer Series in Computational Mathematics ; 60
Zusatzinfo	20 Illustrations, black and white; XIII, 225 p. 20 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	981-19-8531-6 / 9811985316
ISBN-13	978-981-19-8531-7 / 9789811985317
Zustand	Neuware