Hierarchical Matrices: Algorithms and Analysis
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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2015, 2015
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| Edition: | 1st ed. 2015 |
| Series: | Springer Series in Computational Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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