LEADER 04812nam 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 /$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 $aDifferential equations, Partial 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$aAlgorithms. 615 0$aDifferential equations, Partial. 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 LEADER 02728oam 2200613zu 450 001 9910131911503321 005 20210807004756.0 010 $a2-84133-466-X 010 $a2-8218-1743-6 024 7 $a10.4000/books.puc.776 035 $a(CKB)3460000000122183 035 $a(SSID)ssj0001537439 035 $a(PQKBManifestationID)11905280 035 $a(PQKBTitleCode)TC0001537439 035 $a(PQKBWorkID)11519682 035 $a(PQKB)10999565 035 $a(WaSeSS)IndRDA00044728 035 $a(FrMaCLE)OB-puc-776 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/48007 035 $a(PPN)182835855 035 $a(oapen)doab48007 035 $a(EXLCZ)993460000000122183 100 $a20160829d2004 uy 101 0 $afre 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 04$aLes Français sont dans la baie : l'expédition en baie de Bantry, 1796 210 $cPresses universitaires de Caen$d2004 210 31$a[Place of publication not identified]$cPresses universitaires de Caen$d2004 215 $a1 online resource (195 pages) 225 0 $aLitte?rature et civilisation irlandaises 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a2-84133-178-4 330 $aPOUR FRAPPER L?ANGLETERRE et se porter au secours de Wolfe Tone et des Irlandais Unis, la France de la Révolution envoie en Irlande une armée d?invasion commandée par le général Hoche. Mais la tempête et le brouillard empêchent le débarquement et l?expédition de décembre 1796 se solde par un échec. Des chercheurs venus de disciplines très différentes étudient tous les aspects de cette tentative avortée : la stratégie française ; les forces militaires et navales en Grande-Bretagne et en Irlande ; le contexte social ; les données géographiques et le contexte historique ; les attentes exprimées en Irlande, en particulier dans les ballades populaires ; et, bien sûr, le rôle déterminant joué par les conditions météorologiques. 606 $aRegions & Countries - Europe$2HILCC 606 $aHistory & Archaeology$2HILCC 606 $aIreland$2HILCC 607 $aIreland$xHistory$y1760-1820 610 $ahistoire navale 610 $arelations franco-irlandaises 610 $ahistoire militaire 610 $aIrlande 615 7$aRegions & Countries - Europe 615 7$aHistory & Archaeology 615 7$aIreland 700 $aJohn A. Murphy (dir.)$4auth$01356968 702 $aMurphy$b John A. 801 0$bPQKB 906 $aBOOK 912 $a9910131911503321 996 $aLes Français sont dans la baie : l'expédition en baie de Bantry, 1796$93362182 997 $aUNINA