Hierarchical matrices: algorithms and analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2015]
|
| Schriftenreihe: | Springer series in computational mathematics
volume 49 |
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online Ressource (XXV, 511 Seiten, 87 illus., 27 illus. in color) |
| ISBN: | 9783662473245 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-662-47324-5 |
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Datensatz im Suchindex
| _version_ | 1804175846715424768 |
|---|---|
| adam_text | HIERARCHICAL MATRICES: ALGORITHMS AND ANALYSIS
/ HACKBUSCH, WOLFGANG
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
HIERARCHICAL MATRICES: ALGORITHMS AND ANALYSIS
/ HACKBUSCH, WOLFGANG
: 2015
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Hackbusch, Wolfgang 1948- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-47324-5 |
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| isbn | 9783662473245 |
| issn | 0179-3632 |
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| spelling | Hackbusch, Wolfgang 1948- Verfasser (DE-588)115588582 aut Hierarchical matrices: algorithms and analysis Wolfgang Hackbusch Berlin Springer [2015] © 2015 1 Online Ressource (XXV, 511 Seiten, 87 illus., 27 illus. in color) txt rdacontent c rdamedia cr rdacarrier Springer series in computational mathematics volume 49 0179-3632 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 Mathematik Hierarchische Matrix (DE-588)4702093-3 gnd rswk-swf Hierarchische Matrix (DE-588)4702093-3 s DE-604 Erscheint auch als Druckausgabe 978-3-662-47323-8 Springer series in computational mathematics volume 49 (DE-604)BV035421315 49 https://doi.org/10.1007/978-3-662-47324-5 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730338&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730338&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Hackbusch, Wolfgang 1948- Hierarchical matrices: algorithms and analysis Springer series in computational mathematics 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 Mathematik Hierarchische Matrix (DE-588)4702093-3 gnd |
| subject_GND | (DE-588)4702093-3 |
| title | Hierarchical matrices: algorithms and analysis |
| title_auth | Hierarchical matrices: algorithms and analysis |
| title_exact_search | Hierarchical matrices: algorithms and analysis |
| title_full | Hierarchical matrices: algorithms and analysis Wolfgang Hackbusch |
| title_fullStr | Hierarchical matrices: algorithms and analysis Wolfgang Hackbusch |
| title_full_unstemmed | Hierarchical matrices: algorithms and analysis Wolfgang Hackbusch |
| title_short | Hierarchical matrices: algorithms and analysis |
| title_sort | hierarchical matrices algorithms and analysis |
| topic | 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 Mathematik Hierarchische Matrix (DE-588)4702093-3 gnd |
| topic_facet | 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 Mathematik Hierarchische Matrix |
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