Matrix iterative analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2000
|
| Ausgabe: | 2., rev. and expanded ed. |
| Schriftenreihe: | Springer series in computational mathematics
27 |
| Schlagworte: | |
| Online-Zugang: | Table of Contents Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 337 - 353 |
| Beschreibung: | X, 358 S. graph. Darst. 24 cm |
| ISBN: | 3540663215 |
Internformat
MARC
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| 100 | 1 | |a Varga, Richard S. |d 1928-2022 |e Verfasser |0 (DE-588)1068286725 |4 aut | |
| 245 | 1 | 0 | |a Matrix iterative analysis |c Richard S. Varga |
| 250 | |a 2., rev. and expanded ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a X, 358 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in computational mathematics |v 27 | |
| 500 | |a Literaturverz. S. 337 - 353 | ||
| 650 | 7 | |a Análise numérica |2 larpcal | |
| 650 | 7 | |a Equações diferenciais parciais eliticas |2 larpcal | |
| 650 | 7 | |a Equações diferenciais parciais parabólicas |2 larpcal | |
| 650 | 7 | |a Métodos iterativos |2 larpcal | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
| 650 | 4 | |a Matrices | |
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Datensatz im Suchindex
| _version_ | 1804127453737648128 |
|---|---|
| adam_text | Contents
1. Matrix Properties and Concepts 1
1.1 Introduction 1
1.2 A Simple Example 3
1.3 Norms and Spectral Radii 7
1.4 Bounds for the Spectral Radius of a Matrix and Directed
Graphs 16
1.5 Diagonally Dominant Matrices 22
1.6 Ovals of Cassini 24
2. Nonnegative Matrices 31
2.1 Spectral Radii of Nonnegative Matrices 31
2.2 Cyclic and Primitive Matrices 40
2.3 Reducible Matrices 50
2.4 Nonnegative Matrices and Directed Graphs 53
3. Basic Iterative Methods and Comparison Theorems 63
3.1 The Point Jacobi, Gauss Seidel, and Successive Overrelax
ation Iterative Methods 63
3.2 Average Rates of Convergence 68
3.3 The Stein Rosenberg Theorem 74
3.4 The Ostrowski Reich Theorem 81
3.5 Stieltjes Matrices, M Matrices and H Matrices 87
3.6 Regular and Weak Regular Splittings of Matrices 94
4. Successive Overrelaxation Iterative Methods 111
4.1 p Cyclic Matrices 111
4.2 The Successive Overrelaxation Iterative Method for p Cyclic
Matrices 119
4.3 Theoretical Determination of an Optimum Relaxation Factor 123
4.4 Extensions of the 2 Cyclic Theory of Matrices 130
4.5 Asymptotic Rates of Convergence 141
4.6 CO(q,r) and GCO(q,r): Generalized Consistent Orderings .. 143
X Contents
5. Semi Iterative Methods 149
5.1 Semi Iterative Methods and Chebyshev Polynomials 149
5.2 Relationship of Semi Iterative Methods to Successive Overre
laxation Iterative Methods 158
5.3 Comparison of Average Rates of Convergence: the Weakly
Cyclic Case 165
5.4 Cyclic Reduction and Related Iterative Methods 170
5.5 Semi Iterative Methods Applied to the Successive Overrelax
ation Method 174
6. Derivation and Solution of Elliptic Difference Equations .. 183
6.1 A Simple Two Point Boundary Value Problem 183
6.2 General Second Order Ordinary Differential Equations 196
6.3 Derivation of Finite Difference Approximations in Higher Di¬
mensions 204
6.4 Factorization Techniques and Block Iterative Methods 219
6.5 Asymptotic Convergence Rates for the Model Problem 226
7. Alternating Direction Implicit Iterative Methods 235
7.1 The Peaceman Rachford Iterative Method 235
7.2 The Commutative Case 245
7.3 The Noncommutative Case 255
7.4 Variants of the Peaceman Rachford Iterative Method 264
8. Matrix Methods for Parabolic Partial Differential Equa¬
tions 275
8.1 Semi Discrete Approximation 275
8.2 Essentially Positive Matrices 281
8.3 Matrix Approximations for exp( iS) 287
8.4 Relationship with Iterative Methods for Solving Elliptic Dif¬
ference Equations 296
8.5 Chebyshev Rational Approximations for exp( tS) 304
9. Estimation of Acceleration Parameters 313
9.1 Application of the Theory of Nonnegative Matrices 313
9.2 Application of Isoperimetric Inequalities 321
A. Appendix 329
B. Appendix 333
References 337
Index 355
|
| any_adam_object | 1 |
| author | Varga, Richard S. 1928-2022 |
| author_GND | (DE-588)1068286725 |
| author_facet | Varga, Richard S. 1928-2022 |
| author_role | aut |
| author_sort | Varga, Richard S. 1928-2022 |
| author_variant | r s v rs rsv |
| building | Verbundindex |
| bvnumber | BV012782578 |
| callnumber-first | Q - Science |
| callnumber-label | QA297 |
| callnumber-raw | QA297.8.V37 2000 |
| callnumber-search | QA297.8.V37 2000 |
| callnumber-sort | QA 3297.8 V37 42000 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 900 SK 910 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)42619681 (DE-599)BVBBV012782578 |
| dewey-full | 512.9/434 512.9/43421 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 512.9/434 21 |
| dewey-search | 512.9/434 512.9/434 21 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2., rev. and expanded ed. |
| format | Book |
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| id | DE-604.BV012782578 |
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| indexdate | 2024-07-09T18:33:36Z |
| institution | BVB |
| isbn | 3540663215 |
| language | English |
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| physical | X, 358 S. graph. Darst. 24 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spelling | Varga, Richard S. 1928-2022 Verfasser (DE-588)1068286725 aut Matrix iterative analysis Richard S. Varga 2., rev. and expanded ed. Berlin [u.a.] Springer 2000 X, 358 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 27 Literaturverz. S. 337 - 353 Análise numérica larpcal Equações diferenciais parciais eliticas larpcal Equações diferenciais parciais parabólicas larpcal Métodos iterativos larpcal Iterative methods (Mathematics) Matrices Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 s Iteration (DE-588)4123457-1 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s Matrix Mathematik (DE-588)4037968-1 s 1\p DE-604 Springer series in computational mathematics 27 (DE-604)BV000012004 27 http://lcweb.loc.gov/catdir/toc/99050196.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008693810&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Varga, Richard S. 1928-2022 Matrix iterative analysis Springer series in computational mathematics Análise numérica larpcal Equações diferenciais parciais eliticas larpcal Equações diferenciais parciais parabólicas larpcal Métodos iterativos larpcal Iterative methods (Mathematics) Matrices Matrizenrechnung (DE-588)4126963-9 gnd Iteration (DE-588)4123457-1 gnd Matrix Mathematik (DE-588)4037968-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4123457-1 (DE-588)4037968-1 (DE-588)4128130-5 |
| title | Matrix iterative analysis |
| title_auth | Matrix iterative analysis |
| title_exact_search | Matrix iterative analysis |
| title_full | Matrix iterative analysis Richard S. Varga |
| title_fullStr | Matrix iterative analysis Richard S. Varga |
| title_full_unstemmed | Matrix iterative analysis Richard S. Varga |
| title_short | Matrix iterative analysis |
| title_sort | matrix iterative analysis |
| topic | Análise numérica larpcal Equações diferenciais parciais eliticas larpcal Equações diferenciais parciais parabólicas larpcal Métodos iterativos larpcal Iterative methods (Mathematics) Matrices Matrizenrechnung (DE-588)4126963-9 gnd Iteration (DE-588)4123457-1 gnd Matrix Mathematik (DE-588)4037968-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Análise numérica Equações diferenciais parciais eliticas Equações diferenciais parciais parabólicas Métodos iterativos Iterative methods (Mathematics) Matrices Matrizenrechnung Iteration Matrix Mathematik Numerisches Verfahren |
| url | http://lcweb.loc.gov/catdir/toc/99050196.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008693810&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012004 |
| work_keys_str_mv | AT vargarichards matrixiterativeanalysis |