LEADER 04837nam 22007815 450 001 9910300248003321 005 20220329225929.0 010 $a3-662-47324-0 024 7 $a10.1007/978-3-662-47324-5 035 $a(CKB)3710000000541909 035 $a(EBL)4213051 035 $a(SSID)ssj0001597274 035 $a(PQKBManifestationID)16297056 035 $a(PQKBTitleCode)TC0001597274 035 $a(PQKBWorkID)14886358 035 $a(PQKB)10872929 035 $a(DE-He213)978-3-662-47324-5 035 $a(MiAaPQ)EBC4213051 035 $a(PPN)19088553X 035 $a(EXLCZ)993710000000541909 100 $a20151221d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHierarchical matrices: algorithms and analysis$b[electronic resource] /$fby Wolfgang Hackbusch 205 $a1st ed. 2015. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2015. 215 $a1 online resource (532 p.) 225 1 $aSpringer Series in Computational Mathematics,$x0179-3632 ;$v49 300 $aDescription based upon print version of record. 311 $a3-662-47323-2 320 $aIncludes bibliographical references and index. 327 $aPreface -- Part I: Introductory and Preparatory Topics -- 1. Introduction -- 2. Rank-r Matrices -- 3. Introductory Example -- 4. Separable Expansions and Low-Rank Matrices -- 5. Matrix Partition -- Part II: H-Matrices and Their Arithmetic -- 6. Definition and Properties of Hierarchical Matrices -- 7. Formatted Matrix Operations for Hierarchical Matrices -- 8. H2-Matrices -- 9. Miscellaneous Supplements -- Part III: Applications -- 10. Applications to Discretised Integral Operators -- 11. Applications to Finite Element Matrices -- 12. Inversion with Partial Evaluation -- 13. Eigenvalue Problems -- 14. Matrix Functions -- 15. Matrix Equations -- 16. Tensor Spaces -- Part IV: Appendices -- A. Graphs and Trees -- B. Polynomials -- C. Linear Algebra and Functional Analysis -- D. Sinc Functions and Exponential Sums -- E. Asymptotically Smooth Functions -- References -- Index. 330 $aThis self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering. 410 0$aSpringer Series in Computational Mathematics,$x0179-3632 ;$v49 606 $aNumerical analysis 606 $aAlgorithms 606 $aPartial differential equations 606 $aIntegral equations 606 $aMatrix theory 606 $aAlgebra 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aNumerical analysis. 615 0$aAlgorithms. 615 0$aPartial differential equations. 615 0$aIntegral equations. 615 0$aMatrix theory. 615 0$aAlgebra. 615 14$aNumerical Analysis. 615 24$aAlgorithms. 615 24$aPartial Differential Equations. 615 24$aIntegral Equations. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 676 $a512.9434 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 $a9910300248003321 996 $aHierarchical matrices$91522861 997 $aUNINA