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200 10$aNumerical Linear Algebra and Matrix Factorizations /$fby Tom Lyche
205   $a1st ed. 2020.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020.
215   $a1 online resource (XXIII, 371 p. 181 illus., 37 illus. in color.) 
225 1 $aTexts in Computational Science and Engineering,$x1611-0994 ;$v22
311   $a3-030-36467-4 
327   $aA Short Review of Linear Algebra -- LU and QR Factorizations -- Eigenpairs and Singular Values -- Matrix Norms and Least Squares -- Kronecker Products and Fourier Transforms -- Iterative Methods for Large Linear Systems -- Eigenvalues and Eigenvectors -- Index.
330   $aAfter reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
410  0$aTexts in Computational Science and Engineering,$x1611-0994 ;$v22
606   $aMatrix theory
606   $aAlgebra
606   $aAlgorithms
606   $aComputer mathematics
606   $aNumerical analysis
606   $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094
606   $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018
606   $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
615  0$aMatrix theory.
615  0$aAlgebra.
615  0$aAlgorithms.
615  0$aComputer mathematics.
615  0$aNumerical analysis.
615 14$aLinear and Multilinear Algebras, Matrix Theory.
615 24$aAlgorithms.
615 24$aComputational Science and Engineering.
615 24$aNumerical Analysis.
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