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...

Full description

Bibliographic Details
Call Number:Libro Electrónico
Main Author: Hackbusch, Wolfgang (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Series:Springer Series in Computational Mathematics, 49
Subjects:
Numerical analysis.
Algorithms.
Differential equations.
Integral equations.
Algebras, Linear.
Numerical Analysis.
Differential Equations.
Integral Equations.
Linear Algebra.
Online Access:Texto Completo
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.

Similar Items