LEADER 02797nam 2200553 450 001 9910717411903321 005 20231206232413.0 010 $a3-031-25820-7 035 $a(CKB)5720000000183532 035 $a(NjHacI)995720000000183532 035 $a(PPN)269658254 035 $a(MiAaPQ)EBC7243105 035 $a(Au-PeEL)EBL7243105 035 $a(OCoLC)1378390037 035 $a(EXLCZ)995720000000183532 100 $a20230531d2023 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgorithms for Sparse Linear Systems /$fJennifer Scott, Miroslav Tu?ma 205 $a1st ed. 210 1$aCham :$cSpringer International Publishing,$d2023. 215 $a1 online resource (xix, 242 pages) $cillustrations (some color) 225 1 $aNec?as Center Series 311 $a3-031-25819-3 320 $aIncludes bibliographical references and index. 327 $aAn introduction to sparse matrices Sparse matrices and their graphs Introduction to matrix factorizations Sparse Cholesky sovler: The symbolic phase Sparse Cholesky solver: The factorization phase Sparse LU factorizations Stability, ill-conditioning and symmetric indefinite factorizations Sparse matrix ordering algorithms Algebraic preconditioning and approximate factorizations Incomplete factorizations Sparse approximate inverse preconditioners. 330 $aLarge sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. 410 0$aNec?as Center Series. 606 $aAlgorithms$vCongresses 606 $aMatrius disperses$2thub 606 $aSistemes lineals$2thub 606 $aAlgorismes$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgorithms 615 7$aMatrius disperses 615 7$aSistemes lineals 615 7$aAlgorismes 676 $a511.8 700 $aScott$b Jennifer$01359751 702 $aTu?ma$b Miroslav 801 0$bNjHacI 801 1$bNjHacl 906 $aBOOK 912 $a9910717411903321 996 $aAlgorithms for Sparse Linear Systems$93374392 997 $aUNINA