04810nam 22007815 450 991030024800332120220329225929.03-662-47324-010.1007/978-3-662-47324-5(CKB)3710000000541909(EBL)4213051(SSID)ssj0001597274(PQKBManifestationID)16297056(PQKBTitleCode)TC0001597274(PQKBWorkID)14886358(PQKB)10872929(DE-He213)978-3-662-47324-5(MiAaPQ)EBC4213051(PPN)19088553X(EXLCZ)99371000000054190920151221d2015 u| 0engur|n|---|||||txtccrHierarchical matrices: algorithms and analysis /by Wolfgang Hackbusch1st ed. 2015.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2015.1 online resource (532 p.)Springer Series in Computational Mathematics,0179-3632 ;49Description based upon print version of record.3-662-47323-2 Includes bibliographical references and index.Preface -- 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.This 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.Springer Series in Computational Mathematics,0179-3632 ;49Numerical analysisAlgorithmsPartial differential equationsIntegral equationsMatrix theoryAlgebraNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Integral Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12090Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Numerical analysis.Algorithms.Partial differential equations.Integral equations.Matrix theory.Algebra.Numerical Analysis.Algorithms.Partial Differential Equations.Integral Equations.Linear and Multilinear Algebras, Matrix Theory.512.9434Hackbusch Wolfgangauthttp://id.loc.gov/vocabulary/relators/aut51792MiAaPQMiAaPQMiAaPQBOOK9910300248003321Hierarchical matrices1522861UNINA