ABS projection algorithms: mathematical techniques for linear and nonlinear equations
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Horwood u.a.
1989
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Ellis Horwood series in mathematics and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 220 S. |
| ISBN: | 0745804233 0470215070 |
Internformat
MARC
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| 245 | 1 | 0 | |a ABS projection algorithms |b mathematical techniques for linear and nonlinear equations |c Jozsef Abaffy ; Emilio Spedicato |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester u.a. |b Horwood u.a. |c 1989 | |
| 300 | |a 220 S. | ||
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Datensatz im Suchindex
| _version_ | 1804117212901933056 |
|---|---|
| adam_text | Table of contents
Preface 9
1 INTRODUCTION
1.1 Scope and limitations of the monograph 11
1.2 Synopsis 12
1.3 Notation and special definitions 14
2 DERIVATION OF THE ABS ALGORITHM (BASIC FORM)
2.1 Introduction 16
2.2 Heuristic derivation of the ABS algorithm 17
2.3 Bibliographical remarks 20
3 BASIC PROPERTIES OF ITERATES OF THE ABS CLASS
3.1 Introduction 21
3.2 Properties of the matrices Ht 22
3.3 Properties of the search vectors 30
3.4 Properties of the approximation *, to the solution 32
3.5 Updating the solution of a modified system 35
3.6 Bibliographical remarks 37
4 ALTERNATIVE REPRESENTATIONS OF THE SEARCH VECTOR AND
THE MATRIX Ht
4.1 Introduction 38
4.2 Representation ofHi+1 in terms ofHu A and W 38
4.3 Representation of H,,+1 in terms of A and Ht 40
4.4 Representation of/?, in terms of 2i vectors 44
4.5 Representation of/?, in terms of n i vectors 46
4.6 Representation of/?, in terms of i vectors 49
4.7 Bibliographical remarks 49
6 Table of contents
5 THE HUANG AND THE MODIFIED HUANG ALGORITHM
5.1 Introduction 50
5.2 Definition and basic properties of the Huang algorithm 50
5.3 Alternative representation of the Huang and the modified
Huang algorithms 56
5.4 The partial Huang and the modified Huang algorithms 60
5.5 Relationships with the Moore Penrose pseudoinverse 65
5.6 Relationships with the algorithm of Pyle and the algorithm of Brent. .66
5.7 Bibliographical remarks 69
6 THE IMPLICIT GAUSS CHOLESKY (IMPLICIT LV Lt1)
ALGORITHM
6.1 Introduction 70
6.2 Derivation of the parameters that generate an implicit LU
factorization 71
6.3 Properties of the vectors p,.and xt 76
6.4 Derivation of the parameters that generate an implicit LLT
factorization 80
6.5 Alternative representation of the implicit LU factorization algorithm .85
6.6 Relationships with the escalator method, the method of Brown
and the method of Sloboda 88
6.7 Computing the inverse by the implicit LU factorization algorithm . . .90
6.8 Bibliographical remarks 92
7 THE SCALED ABS ALGORITHM: GENERAL FORMULATION
7.1 Introduction 93
7.2 Derivation of the scaled ABS algorithm 93
7.3 Basic properties of the scaled ABS class 95
7.4 Alternative formulations of the scaled ABS algorithm 97
7.5 Block formulation of the scaled ABS algorithm 98
7.6 Semiconjugate and biconjugate ABS algorithms: equivalence
relations and variational characterization 105
7.7 Relationships with the Stewart generalized conjugate direction
algorithm 110
7.8 Relationships with the Broyden general finitely terminating algorithm 113
7.9 Bibliographical remarks 116
8 SUBCLASSES IN THE SCALED ABS ALGORITHM
8.1 Introduction 117
8.2 Subclass SI: the scaled symmetric and the scaled Huang algorithms . 118
8.3 Subclass S2: the class of the conjugate direction ABS algorithms ... 123
8.4 Subclass S3: the orthogonally scaled ABS algorithms 129
8.5 Subclass S4: the class of the optimally stable ABS algorithms 135
8.6 Subclass S5: the Voyevodin class of conjugate gradient type
algorithms 142
Table of contents 7
8.7 Subclass S6: the Hegedus Bodocs class of biorthogonalization
algorithms 146
8.8 Subclass S7: the ABS class of ^ conjugate residuals 149
8.9 Subclass S8: a class of ABS updates factorizing A into lower
Hessenberg form 150
8.10 Bibliographical remarks 152
9 LEAST SQUARES SOLUTION OF OVERDETERMINED LINEAR
SYSTEMS
9.1 Introduction 153
9.2 Solution in n + m steps via the Huang algorithm on an extended system 154
9.3 Solution in n steps via a subclass of the scaled ABS algorithm 155
9.4 Solution by explicit construction of orthogonal factorizations 156
9.5 Solution via explicit evaluation of the Moore Penrose pseudoinverse 158
9.6 Bibliographical remarks 160
10 COMPUTATIONAL PERFORMANCE OF THE MODIFIED HUANG
ALGORITHM ON LINEAR SYSTEMS AND LINEAR LEAST SQUARES
10.1 Introduction 161
10.2 Performance of the Huang and the modified Huang algorithms on
linear systems 162
10.3 Performance of the modified Huang algorithm on linear least
squares 166
10.4 Bibliographical remarks 171
11 APPLICATION OF THE IMPLICIT LU, LQ AND QR ALGORITHMS
TO SOME SPARSE LARGE LINEAR SYSTEMS
11.1 Introduction 172
11.2 Application of the implicit LU algorithm to ND matrices 173
11.3 Application of the implicit LU, QR and LQ algorithms to
banded type matrices 177
11.4 Bibliographical remarks 180
12 ERROR ANALYSIS IN THE SCALED ABS ALGORITHM
12.1 Introduction 181
12.2 Sensitivity analysis via the Broyden approach 181
12.3 Forward error analysis in floating point arithmetic 188
12.4 Bibliographical remarks 191
13 THE ABS ALGORITHM FOR NONLINEAR SYSTEMS
13.1 Introduction 192
13.2 Formulation of the scaled block nonlinear ABS algorithm 193
13.3 Local convergence of the scaled block nonlinear ABS algorithm. . . 195
13.4 Special cases of the scaled block nonlinear ABS algorithm 198
8 Table of contents
13.5 Another g superlinear convergence theorem 202
13.6 Numerical experiments 204
13.7 Final remarks 206
13.8 Bibliographical remarks 206
References 208
Author index 216
Subject index 218
|
| any_adam_object | 1 |
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| building | Verbundindex |
| bvnumber | BV002919045 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.58 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 915 |
| classification_tum | MAT 663f MAT 657f |
| ctrlnum | (OCoLC)246789333 (DE-599)BVBBV002919045 |
| dewey-full | 511.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.8 |
| dewey-search | 511.8 |
| dewey-sort | 3511.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| genre | ABS-Methode gnd |
| genre_facet | ABS-Methode |
| id | DE-604.BV002919045 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:50:49Z |
| institution | BVB |
| isbn | 0745804233 0470215070 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001827419 |
| oclc_num | 246789333 |
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| physical | 220 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Horwood u.a. |
| record_format | marc |
| series2 | Ellis Horwood series in mathematics and its applications |
| spelling | Abaffy, Jozsef Verfasser aut ABS projection algorithms mathematical techniques for linear and nonlinear equations Jozsef Abaffy ; Emilio Spedicato 1. publ. Chichester u.a. Horwood u.a. 1989 220 S. txt rdacontent n rdamedia nc rdacarrier Ellis Horwood series in mathematics and its applications ABS-Methode gnd rswk-swf ABS-Methode f DE-604 Spedicato, Emilio Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001827419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abaffy, Jozsef Spedicato, Emilio ABS projection algorithms mathematical techniques for linear and nonlinear equations |
| title | ABS projection algorithms mathematical techniques for linear and nonlinear equations |
| title_auth | ABS projection algorithms mathematical techniques for linear and nonlinear equations |
| title_exact_search | ABS projection algorithms mathematical techniques for linear and nonlinear equations |
| title_full | ABS projection algorithms mathematical techniques for linear and nonlinear equations Jozsef Abaffy ; Emilio Spedicato |
| title_fullStr | ABS projection algorithms mathematical techniques for linear and nonlinear equations Jozsef Abaffy ; Emilio Spedicato |
| title_full_unstemmed | ABS projection algorithms mathematical techniques for linear and nonlinear equations Jozsef Abaffy ; Emilio Spedicato |
| title_short | ABS projection algorithms |
| title_sort | abs projection algorithms mathematical techniques for linear and nonlinear equations |
| title_sub | mathematical techniques for linear and nonlinear equations |
| topic_facet | ABS-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001827419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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