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024 7 $a10.1007/978-981-19-8532-4
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101 0 $aeng
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200 10$aKrylov Subspace Methods for Linear Systems$b[electronic resource] $ePrinciples of Algorithms /$fby Tomohiro Sogabe
205   $a1st ed. 2022.
210  1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2022.
215   $a1 online resource (233 pages)
225 1 $aSpringer Series in Computational Mathematics,$x2198-3712 ;$v60
300   $aIncludes index.
311 08$aPrint version: Sogabe, Tomohiro Krylov Subspace Methods for Linear Systems Singapore : Springer,c2023 9789811985317 
327   $aIntroduction to Numerical Methods for Solving Linear Systems -- Some Applications to Computational Science and Data Science -- Classi?cation and Theory of Krylov Subspace Methods -- Applications to Shifted Linear Systems -- Applications to Matrix Functions.
330   $aThis book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.
410  0$aSpringer Series in Computational Mathematics,$x2198-3712 ;$v60
606   $aNumerical analysis
606   $aMathematical models
606   $aAlgorithms
606   $aNumerical Analysis
606   $aMathematical Modeling and Industrial Mathematics
606   $aAlgorithms
615  0$aNumerical analysis.
615  0$aMathematical models.
615  0$aAlgorithms.
615 14$aNumerical Analysis.
615 24$aMathematical Modeling and Industrial Mathematics.
615 24$aAlgorithms.
676   $a518.1
700   $aSogabe$b Tomohiro$01275249
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a996508571203316
996   $aKrylov Subspace Methods for Linear Systems$93004752
997   $aUNISA