Hierarchical Matrices: Algorithms and Anal...

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Beschreibung

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 hierarchicalmatrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

Über den Autor

The author is a very well-known author of Springer, working in the field of numerical mathematics for partial differential equations and integral equations. He has published numerous books in the SSCM series, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and a book in German about the technique of hierarchical matrices. Hackbusch is member of the editorial board of Springer' s book series "Advances in Numerical Mathematics", "The International Cryogenics Monograph Series" and has now joined as new member of the editorial board of "Springer Series of Computational Mathematics".

Zusammenfassung

Matrix algorithms of almost linear cost

Application to matrix equations and matrix functions

Self-contained contents by means of five appendices

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2019
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Series in Computational Mathematics
Inhalt:	xxv 511 S. 60 s/w Illustr. 27 farbige Illustr. 511 p. 87 illus. 27 illus. in color.
ISBN-13:	9783662568941
ISBN-10:	3662568942
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Hackbusch, Wolfgang
Auflage:	Softcover reprint of the original 1st ed. 2015
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Springer Series in Computational Mathematics
Maße:	235 x 155 x 29 mm
Von/Mit:	Wolfgang Hackbusch
Erscheinungsdatum:	14.03.2019
Gewicht:	0,809 kg

Artikel-ID: 115104507