03650nam 22006015 450 99650857120331620230120100921.09789811985324(electronic bk.)978981198531710.1007/978-981-19-8532-4(MiAaPQ)EBC7184760(Au-PeEL)EBL7184760(CKB)26037408400041(MiAaPQ)EBC7184755(DE-He213)978-981-19-8532-4(PPN)26780749X(EXLCZ)992603740840004120230120d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierKrylov Subspace Methods for Linear Systems[electronic resource] Principles of Algorithms /by Tomohiro Sogabe1st ed. 2022.Singapore :Springer Nature Singapore :Imprint: Springer,2022.1 online resource (233 pages)Springer Series in Computational Mathematics,2198-3712 ;60Includes index.Print version: Sogabe, Tomohiro Krylov Subspace Methods for Linear Systems Singapore : Springer,c2023 9789811985317 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.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.Springer Series in Computational Mathematics,2198-3712 ;60Numerical analysisMathematical modelsAlgorithmsNumerical AnalysisMathematical Modeling and Industrial MathematicsAlgorithmsNumerical analysis.Mathematical models.Algorithms.Numerical Analysis.Mathematical Modeling and Industrial Mathematics.Algorithms.518.1Sogabe Tomohiro1275249MiAaPQMiAaPQMiAaPQ996508571203316Krylov Subspace Methods for Linear Systems3004752UNISA