LEADER 03804nam 2200553 450 001 996418198403316 005 20220318154559.0 010 $a3-030-59789-X 024 7 $a10.1007/978-3-030-59789-4 035 $a(CKB)4100000011558643 035 $a(DE-He213)978-3-030-59789-4 035 $a(MiAaPQ)EBC6383600 035 $a(MiAaPQ)EBC6647489 035 $a(Au-PeEL)EBL6383600 035 $a(OCoLC)1225893605 035 $a(Au-PeEL)EBL6647489 035 $a(PPN)25250772X 035 $a(EXLCZ)994100000011558643 100 $a20220318d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExercises in numerical linear algebra and matrix factorizations /$fTom Lyche, Georg Muntingh, and Øyvind Ryan 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XIX, 265 p. 12 illus., 10 illus. in color.) 225 1 $aTexts in Computational Science and Engineering,$x1611-0994 ;$v23 311 $a3-030-59788-1 327 $aA Short Review of Linear Algebra -- Diagonally Dominant Tridiagonal Matrices; Three Examples -- Gaussian Eliminationa nd LU Factorizations -- LDL* Factorization and Positive Definite Matrices -- Orthonormal and Unitary Transformations -- Eigenpairs and Similarity Transformations -- The Singular Value Decomposition -- Matrix Norms and Perturbation Theory for Linear Systems -- Least Squares -- The Kronecker Product -- Fast Direct Solution of a Large Linear System -- The Classical Iterative Methods -- The Conjugate Gradient Method -- Numerical Eigenvalue Problems -- The QR Algorithm. 330 $aTo put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students? learning process. This book provides precisely this type of supporting material for the textbook ?Numerical Linear Algebra and Matrix Factorizations,? published as Vol. 22 of Springer?s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels. 410 0$aTexts in Computational Science and Engineering,$x1611-0994 ;$v23 606 $aAlgebras, Linear 606 $aComputer science$xMathematics 615 0$aAlgebras, Linear. 615 0$aComputer science$xMathematics. 676 $a512.5 700 $aLyche$b Tom$060177 702 $aMuntingh$b Georg 702 $aRyan$b Øyvind 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418198403316 996 $aExercises in Numerical Linear Algebra and Matrix Factorizations$91889144 997 $aUNISA