Hierarchical Matrices: Algorithms and Analysis

• Κύριος συγγραφέας: Hackbusch, Wolfgang (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Σειρά: Springer Series in Computational Mathematics, 49
• Θέματα: Mathematics.; Matrix theory.; Algebra.; Integral equations.; Partial differential equations.; Algorithms.; Numerical analysis.; Numerical Analysis.; Partial Differential Equations.; Integral Equations.; Linear and Multilinear Algebras, Matrix Theory.

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...

Πίνακας περιεχομένων:

• 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.