Hierarchical Matrices: Algorithms and Analysis

AvWolfgang Hackbusch

Inbunden, Engelska, 2015

Del 49 i serien Springer Series in Computational Mathematics

1 107 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Häftad

1 107 kr

Skickas inom 5-8 vardagar

Beskrivning

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.

Produktinformation

Utgivningsdatum:2015-12-21
Mått:155 x 235 x 35 mm
Vikt:969 g
Format:Inbunden
Språk:Engelska
Serie:Springer Series in Computational Mathematics
Antal sidor:511
Upplaga:15001
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783662473238

Utforska kategorier

Mer om författaren

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".

Recensioner i media

"The book 'Hierarchical matrices: algorithms and analysis' is a self-contained monograph which presents an efficient possibility to handle the numerical treatment of fully populated large scale matrices appearing in scientific computations, and therefore it is of interest to scientists in computational mathematics, physics, chemistry and engineering." (Constantin Popa, zbMATH 1336.65041, 2016)

Innehållsförteckning

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.