Hierarchical Matrices: Algorithms and Analysis / by Wolfgang Hackbusch
データ種別 | 電子書籍 |
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版 | 1st ed. 2015. |
出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2015 |
書誌詳細を非表示
書誌ID | OB01016663 |
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本文言語 | 英語 |
一般注記 | 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. License restrictions may limit access Summary: 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 hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering |
著者標目 | *Hackbusch, Wolfgang SpringerLink (Online service) |
統一書名標目 | Springer Series in Computational Mathematics, |
件 名 | LCSH:Mathematics LCSH:Matrix theory LCSH:Algebra LCSH:Integral equations LCSH:Partial differential equations LCSH:Algorithms LCSH:Numerical analysis FREE:Mathematics FREE:Numerical Analysis FREE:Algorithms FREE:Partial Differential Equations FREE:Integral Equations FREE:Linear and Multilinear Algebras, Matrix Theory |
分 類 | LCC:QA297-299.4 DC23:518 |
巻冊次 | ISBN:9783662473245 RefWorks出力(各巻) print ; ISBN:9783662473238 RefWorks出力(各巻) |
資料種別 | 機械可読データファイル |
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※2020年8月16日以降