Direct methods for sparse linear systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM
2006
|
| Series: | Fundamentals of algorithms
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 217 S. |
| ISBN: | 0898716136 9780898716139 |
Staff View
MARC
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| 100 | 1 | |a Davis, Timothy A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Direct methods for sparse linear systems |c Timothy A. Davis |
| 264 | 1 | |a Philadelphia |b SIAM |c 2006 | |
| 300 | |a XII, 217 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Fundamentals of algorithms |v 2 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Matrices éparses | |
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Record in the Search Index
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| adam_text | Contents
Preface
xi
1
Introduction
1
1.1
Linear
algebra
............................ 2
1.2
Graph theory, algorithms, and data structures
.......... 4
1.3
Further reading
........................... 6
2
Basic algorithms
7
2.1
Sparse matrix data structures
................... 7
2.2
Matrix-vector multiplication
.................... 9
2.3
Utilities
................................ 10
2.4
Triplet form
............................. 12
2.5
Transpose
................,............. 14
2.6
Summing up duplicate entries
................... 15
2.7
Removing entries from a matrix
.................. 16
2.8
Matrix multiplication
........................ 17
2.9
Matrix addition
........................... 19
2.10
Vector permutation
......................... 20
2.11
Matrix permutation
......................... 21
2.12
Matrix norm
............................. 22
2.13
Reading a matrix from a file
.................... 23
2.14
Printing a matrix
.......................... 23
2.15
Sparse matrix collections
...................... 24
2.16
Further reading
........................... 24
Exercises
................................... 24
3
Solving triangular systems
27
3.1
A dense right-hand side
....................... 27
3.2
A sparse right-hand side
...................... 29
3.3
Further reading
........................... 35
Exercises
................................... 35
4
Chołesky
factorization
37
4.1
Elimination tree
........................... 38
vii
viii Contents
4.2
Sparse
triangular
solve
....................... 43
4.3
Postordering
a tree
......................... 44
4.4
Row counts
.............................. 46
4.5
Column counts
............................ 52
4.6
Symbolic analysis
.......................... 56
4.7
Up-looking Cholesky
........................ 58
4.8
Left-looking and supernodal Cholesky
............... 60
4.9
Right-looking and multifrontal Cholesky
............. 62
4.10
Modifying a Cholesky factorization
................ 63
4.11
Further reading
........................... 66
Exercises
................................... 67
5
Orthogonal methods
69
5.1
Householder reflections
....................... 69
5.2
Left- and right-looking QR factorization
............. 70
5.3
Householder-based sparse QR factorization
............ 71
5.4
Givens
rotations
........................... 79
5.5
Row-merge sparse QR factorization
................ 79
5.6
Further reading
........................... 81
Exercises
................................... 82
6
LU
factorization.
83
6.1
Upper bound on fill-in
....................... 83
6.2
Left-looking
LU
........................... 85
6.3
Right-looking and multifrontal
LU
................. 88
6.4
Further reading
........................... 94
Exercises
................................... 95
7
Fill-reducing
orderings
99
7.1
Minimum degree ordering
...................... 99
7.2
Maximum matching
......................... 112
7.3
Block triangular form
........................ 118
7.4
Dulmage-Mendelsohn decomposition
............... 122
7.5
Bandwidth and profile reduction
.................. 127
7.6
Nested dissection
.......................... 128
7.7
Further reading
........................... 130
Exercises
................................... 133
8
Solving sparse linear systems
135
8.1
Using a Cholesky factorization
................... 135
8.2
Using a QR factorization
...................... 136
8.3
Using an
LU
factorization
..................... 138
8.4
Using a Dulmage-Mendelsohn decomposition
........... 138
8.5
MATLAB
sparse backslash
..................... 140
8.6
Software for solving sparse linear systems
............. 141
Exercises
................................... 144
Contents ix
9 CSparse 145
9.1
Primary CSparse routines and definitions
.............146
9.2
Secondary CSparse routines and definitions
............149
9.3
Tertiary CSparse routines and definitions
.............154
9.4
Examples
...............................158
10
Sparse matrices in
MATLAB
169
10.1
Creating sparse matrices
...................... 169
10.2
Sparse matrix functions and operators
.............. 172
10.3
CSparse
MATLAB
interface
.................... 176
10.4
Examples
............................... 182
10.5
Further reading
........................... 186
Exercises
................................... 186
A Basics of the
С
programming language
187
Bibliography
195
Index
211
|
| adam_txt |
Contents
Preface
xi
1
Introduction
1
1.1
Linear
algebra
. 2
1.2
Graph theory, algorithms, and data structures
. 4
1.3
Further reading
. 6
2
Basic algorithms
7
2.1
Sparse matrix data structures
. 7
2.2
Matrix-vector multiplication
. 9
2.3
Utilities
. 10
2.4
Triplet form
. 12
2.5
Transpose
.,. 14
2.6
Summing up duplicate entries
. 15
2.7
Removing entries from a matrix
. 16
2.8
Matrix multiplication
. 17
2.9
Matrix addition
. 19
2.10
Vector permutation
. 20
2.11
Matrix permutation
. 21
2.12
Matrix norm
. 22
2.13
Reading a matrix from a file
. 23
2.14
Printing a matrix
. 23
2.15
Sparse matrix collections
. 24
2.16
Further reading
. 24
Exercises
. 24
3
Solving triangular systems
27
3.1
A dense right-hand side
. 27
3.2
A sparse right-hand side
. 29
3.3
Further reading
. 35
Exercises
. 35
4
Chołesky
factorization
37
4.1
Elimination tree
. 38
vii
viii Contents
4.2
Sparse
triangular
solve
. 43
4.3
Postordering
a tree
. 44
4.4
Row counts
. 46
4.5
Column counts
. 52
4.6
Symbolic analysis
. 56
4.7
Up-looking Cholesky
. 58
4.8
Left-looking and supernodal Cholesky
. 60
4.9
Right-looking and multifrontal Cholesky
. 62
4.10
Modifying a Cholesky factorization
. 63
4.11
Further reading
. 66
Exercises
. 67
5
Orthogonal methods
69
5.1
Householder reflections
. 69
5.2
Left- and right-looking QR factorization
. 70
5.3
Householder-based sparse QR factorization
. 71
5.4
Givens
rotations
. 79
5.5
Row-merge sparse QR factorization
. 79
5.6
Further reading
. 81
Exercises
. 82
6
LU
factorization.
83
6.1
Upper bound on fill-in
. 83
6.2
Left-looking
LU
. 85
6.3
Right-looking and multifrontal
LU
. 88
6.4
Further reading
. 94
Exercises
. 95
7
Fill-reducing
orderings
99
7.1
Minimum degree ordering
. 99
7.2
Maximum matching
. 112
7.3
Block triangular form
. 118
7.4
Dulmage-Mendelsohn decomposition
. 122
7.5
Bandwidth and profile reduction
. 127
7.6
Nested dissection
. 128
7.7
Further reading
. 130
Exercises
. 133
8
Solving sparse linear systems
135
8.1
Using a Cholesky factorization
. 135
8.2
Using a QR factorization
. 136
8.3
Using an
LU
factorization
. 138
8.4
Using a Dulmage-Mendelsohn decomposition
. 138
8.5
MATLAB
sparse backslash
. 140
8.6
Software for solving sparse linear systems
. 141
Exercises
. 144
Contents ix
9 CSparse 145
9.1
Primary CSparse routines and definitions
.146
9.2
Secondary CSparse routines and definitions
.149
9.3
Tertiary CSparse routines and definitions
.154
9.4
Examples
.158
10
Sparse matrices in
MATLAB
169
10.1
Creating sparse matrices
. 169
10.2
Sparse matrix functions and operators
. 172
10.3
CSparse
MATLAB
interface
. 176
10.4
Examples
. 182
10.5
Further reading
. 186
Exercises
. 186
A Basics of the
С
programming language
187
Bibliography
195
Index
211 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:27:10Z |
| indexdate | 2024-07-09T20:42:47Z |
| institution | BVB |
| isbn | 0898716136 9780898716139 |
| language | English |
| lccn | 2006044387 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014946854 |
| oclc_num | 300527488 |
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| physical | XII, 217 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | SIAM |
| record_format | marc |
| series | Fundamentals of algorithms |
| series2 | Fundamentals of algorithms |
| spelling | Davis, Timothy A. Verfasser aut Direct methods for sparse linear systems Timothy A. Davis Philadelphia SIAM 2006 XII, 217 S. txt rdacontent n rdamedia nc rdacarrier Fundamentals of algorithms 2 Includes bibliographical references and index MATLAB inriac Matrices éparses Matrices éparses ram Systèmes linéaires Systèmes linéaires ram factorisation matrice inriac matrice creuse inriac Sparse matrices Linear systems Direkte Methode (DE-588)4705893-6 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 s Lineares Gleichungssystem (DE-588)4035826-4 s Direkte Methode (DE-588)4705893-6 s DE-604 Fundamentals of algorithms 2 (DE-604)BV017480576 2 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014946854&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davis, Timothy A. Direct methods for sparse linear systems Fundamentals of algorithms MATLAB inriac Matrices éparses Matrices éparses ram Systèmes linéaires Systèmes linéaires ram factorisation matrice inriac matrice creuse inriac Sparse matrices Linear systems Direkte Methode (DE-588)4705893-6 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd |
| subject_GND | (DE-588)4705893-6 (DE-588)4056053-3 (DE-588)4035826-4 |
| title | Direct methods for sparse linear systems |
| title_auth | Direct methods for sparse linear systems |
| title_exact_search | Direct methods for sparse linear systems |
| title_exact_search_txtP | Direct methods for sparse linear systems |
| title_full | Direct methods for sparse linear systems Timothy A. Davis |
| title_fullStr | Direct methods for sparse linear systems Timothy A. Davis |
| title_full_unstemmed | Direct methods for sparse linear systems Timothy A. Davis |
| title_short | Direct methods for sparse linear systems |
| title_sort | direct methods for sparse linear systems |
| topic | MATLAB inriac Matrices éparses Matrices éparses ram Systèmes linéaires Systèmes linéaires ram factorisation matrice inriac matrice creuse inriac Sparse matrices Linear systems Direkte Methode (DE-588)4705893-6 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd |
| topic_facet | MATLAB Matrices éparses Systèmes linéaires factorisation matrice matrice creuse Sparse matrices Linear systems Direkte Methode Schwach besetzte Matrix Lineares Gleichungssystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014946854&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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