LEADER 03847nam 22006015 450 001 9910254096203321 005 20200706132658.0 010 $a3-319-28483-5 024 7 $a10.1007/978-3-319-28483-5 035 $a(CKB)3710000000734694 035 $a(DE-He213)978-3-319-28483-5 035 $a(MiAaPQ)EBC4562172 035 $a(PPN)194378969 035 $a(EXLCZ)993710000000734694 100 $a20160621d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIterative Solution of Large Sparse Systems of Equations /$fby Wolfgang Hackbusch 205 $a2nd ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XXIII, 509 p. 26 illus., 11 illus. in color.) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v95 311 $a3-319-28481-9 320 $aIncludes bibliographical references and index. 327 $aPart I: Linear Iterations -- Introduction -- Iterative Methods -- Classical Linear Iterations in the Positive Definite Case -- Analysis of Classical Iterations Under Special Structural Conditions -- Algebra of Linear Iterations -- Analysis of Positive Definite Iterations -- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods -- Semi-Iterative Methods -- Gradient Methods -- Conjugate Gradient Methods and Generalizations -- Part III: Special Iterations -- Multigrid Iterations -- Domain Decomposition and Subspace Methods -- H-LU Iteration -- Tensor-based Methods -- Appendices. 330 $aIn the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v95 606 $aNumerical analysis 606 $aMatrix theory 606 $aAlgebra 606 $aPartial differential equations 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aNumerical analysis. 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aPartial differential equations. 615 14$aNumerical Analysis. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aPartial Differential Equations. 676 $a518.26 700 $aHackbusch$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$051792 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254096203321 996 $aITERATIVE SOLUTION OF LARGE SPARSE SYSTEMS OF EQUATIONS$9315879 997 $aUNINA