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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
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:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Hackbusch, Wolfgang.  |e author. 
245 1 0 |a Hierarchical Matrices: Algorithms and Analysis  |h [electronic resource] /  |c by Wolfgang Hackbusch. 
250 |a 1st ed. 2015. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2015. 
300 |a XXV, 511 p. 87 illus., 27 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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490 1 |a Springer Series in Computational Mathematics,  |x 0179-3632 ;  |v 49 
505 0 |a 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. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Matrix theory. 
650 0 |a Algebra. 
650 0 |a Integral equations. 
650 0 |a Partial differential equations. 
650 0 |a Algorithms. 
650 0 |a Numerical analysis. 
650 1 4 |a Mathematics. 
650 2 4 |a Numerical Analysis. 
650 2 4 |a Algorithms. 
650 2 4 |a Partial Differential Equations. 
650 2 4 |a Integral Equations. 
650 2 4 |a Linear and Multilinear Algebras, Matrix Theory. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783662473238 
830 0 |a Springer Series in Computational Mathematics,  |x 0179-3632 ;  |v 49 
856 4 0 |u http://dx.doi.org/10.1007/978-3-662-47324-5  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)