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Catalogue Information
Field name	Details
Dewey Class	518
Title	Hierarchical Matrices: Algorithms and Analysis ([EBook]) / by Wolfgang Hackbusch.
Author	Hackbusch, Wolfgang. , 1948-
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Berlin, Heidelberg : Springer , 2015.
Physical Details	XXV, 511 pages, 87 illus., 27 illus. in color. : online resource.
Series	Springer Series in Computational Mathematics 0179-3632 ; ; 49
ISBN	9783662473245
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-662-47324-5
Links to Related Works	Subject References: Algebra . Algorithms . Integral Equations . Linear and Multilinear Algebras, Matrix Theory . Matrix theory . Numerical Analysis . Partial differential equations . Authors: Hackbusch, Wolfgang. 1948- . Corporate Authors: SpringerLink (Online service) . Series: Springer Series in Computational Mathematics . Classification: 518 . 518 (DDC 23) .

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Hierarchical Matrices: Algorithms and Analysis

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