Direct methods for sparse matrices:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2017
|
| Edition: | Second edition |
| Series: | Numerical mathematics and scientific computation
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xx, 429 Seiten Illustrationen |
| ISBN: | 9780198508380 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV043868947 | ||
| 003 | DE-604 | ||
| 005 | 20170315 | ||
| 007 | t | ||
| 008 | 161109s2017 a||| |||| 00||| eng d | ||
| 020 | |a 9780198508380 |9 978-0-19-850838-0 | ||
| 035 | |a (OCoLC)973553755 | ||
| 035 | |a (DE-599)BVBBV043868947 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-703 |a DE-91G |a DE-19 |a DE-20 | ||
| 050 | 0 | |a QA188 | |
| 082 | 0 | |a 512.9/434 |2 19 | |
| 084 | |a SK 220 |0 (DE-625)143224: |2 rvk | ||
| 084 | |a MAT 659f |2 stub | ||
| 084 | |a 65F30 |2 msc | ||
| 084 | |a 65F05 |2 msc | ||
| 100 | 1 | |a Duff, Iain S. |4 aut | |
| 245 | 1 | 0 | |a Direct methods for sparse matrices |c I. S. Duff (Rutherford Appleton Laboratory, CERFACS, Toulouse, France, and Strathclyde University), A. M. Erisman (The Boeing Company, Seattle (retired) and Seattle Pacific University), J. K. Reid (Rutherford Appleton Laboratory and Cranfield University) |
| 250 | |a Second edition | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2017 | |
| 300 | |a xx, 429 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Numerical mathematics and scientific computation | |
| 650 | 4 | |a Algebra - Sparse matrices - Solution - Applications of computer systems | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Sparse matrices |x Data processing | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Datenverarbeitung |0 (DE-588)4011152-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schwach besetzte Matrix |0 (DE-588)4056053-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Schwach besetzte Matrix |0 (DE-588)4056053-3 |D s |
| 689 | 0 | 1 | |a Datenverarbeitung |0 (DE-588)4011152-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Schwach besetzte Matrix |0 (DE-588)4056053-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Schwach besetzte Matrix |0 (DE-588)4056053-3 |D s |
| 689 | 2 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Erisman, Albert M. |4 aut | |
| 700 | 1 | |a Reid, John Ker |d 1938- |0 (DE-588)129926469 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029278861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029278861 | ||
Record in the Search Index
| _version_ | 1804176755570769920 |
|---|---|
| adam_text | Titel: Direct methods for sparse matrices
Autor: Duff, Iain S
Jahr: 2017
CONTENTS
1 Introduction 1
1.1 Introduction 1
1.2 Graph theory 2
1.3 Example of a sparse matrix 5
1.4 Modern computer architectures 10
1.5 Computational performance 12
1.6 Problem formulation 13
1.7 Sparse matrix test collections 14
2 Sparse matrices: storage schemes and simple
operations 18
2.1 Introduction 18
2.2 Sparse vector storage 18
2.3 Inner product of two packed vectors 20
2.4 Adding packed vectors 20
2.5 Use of full-sized arrays 22
2.6 Coordinate scheme for storing sparse matrices 22
2.7 Sparse matrix as a collection of sparse vectors 23
2.8 Sherman s compressed index scheme 25
2.9 Linked lists 26
2.10 Sparse matrix in column-linked list 29
2.11 Sorting algorithms 30
2.11.1 The counting sort 30
2.11.2 Heap sort 31
2.12 Transforming the coordinate scheme to other forms 32
2.13 Access by rows and columns 34
2.14 Supervariables 35
2.15 Matrix by vector products 36
2.16 Matrix by matrix products 36
2.17 Permutation matrices 37
2.18 Clique (or finite-element) storage 39
2.19 Comparisons between sparse matrix structures 40
3 Gaussian elimination for dense matrices: the algebraic
problem 43
3.1 Introduction 43
3.2 Solution of triangular systems 43
3.3 Gaussian elimination 44
3.4 Required row interchanges 46
3.5 Relationship with LU factorization 47
3.6 Dealing with interchanges 49
3.7 LU factorization of a rectangular matrix 49
3.8 Computational sequences, including blocking 50
3.9 Symmetric matrices 52
3.10 Multiple right-hand sides and inverses 54
3.11 Computational cost 55
3.12 Partitioned factorization 57
3.13 Solution of block triangular systems 59
4 Gaussian elimination for dense matrices: numerical
considerations 62
4.1 Introduction 62
4.2 Computer arithmetic error 63
4.3 Algorithm instability 65
4.4 Controlling algorithm stability through pivoting 67
4.4.1 Partial pivoting 67
4.4.2 Threshold pivoting 68
4.4.3 Rook pivoting 68
4.4.4 Pull pivoting 69
4.4.5 The choice of pivoting strategy 70
4.5 Orthogonal factorization 70
4.6 Partitioned factorization 70
4.7 Monitoring the stability 71
4.8 Special stability considerations 72
4.9 Solving indefinite symmetric systems 74
4.10 Ill-conditioning: introduction 74
4.11 Ill-conditioning: theoretical discussion 75
4.12 Ill-conditioning: automatic detection 79
4.12.1 The LINPACK condition estimator 79
4.12.2 Hager s method 80
4.13 Iterative refinement 80
4.14 Scaling 81
4.15 Automatic scaling 83
4.15.1 Scaling so that all entries are close to one 84
4.15.2 Scaling norms 84
4.15.3 I-matrix scaling 85
5 Gaussian elimination for sparse matrices: an
introduction 89
5.1 Introduction 89
5.2 Numerical stability in sparse Gaussian elimination 90
5.2.1 Trade-offs between numerical stability and
sparsity 90
5.2.2 Incorporating rook pivoting 92
5.2.3 2x2 pivoting 93
5.2.4 Other stability considerations 93
5.2.5 Estimating condition numbers in sparse
computation 94
5.3 Orderings 94
5.3.1 Block triangular matrix 95
5.3.2 Local pivot strategies 96
5.3.3 Band and variable band ordering 96
5.3.4 Dissection 98
5.4 Features of a code for the solution of sparse equations 99
5.4.1 Input of data 101
5.4.2 The ANALYSE phase 101
5.4.3 The FACTORIZE phase 101
5.4.4 The SOLVE phase 102
5.4.5 Output of data and analysis of results 103
5.5 Relative work required by each phase 103
5.6 Multiple right-hand sides 104
5.7 Computation of entries of the inverse 105
5.8 Matrices with complex entries 106
5.9 Writing compared with using sparse matrix software 106
6 Reduction to block triangular form 108
6.1 Introduction 108
6.2 Finding the block triangular form in three stages 109
6.3 Looking for row and column singletons 110
6.4 Finding a transversal 111
6.4.1 Background 111
6.4.2 Transversal extension by depth-first search 113
6.4.3 Analysis of the depth-first search transversal
algorithm 115
6.4.4 Implementation of the transversal algorithm 116
6.5 Symmetric permutations to block triangular form 118
6.5.1 Background 118
6.5.2 The algorithm of Sargent and Westerberg 119
6.5.3 Tarjan s algorithm 122
6.5.4 Implementation of Tarjan s algorithm 125
6.6 Essential uniqueness of the block triangular form 125
6.7 Experience with block triangular forms 127
6.8 Maximum transversals 128
6.9 Weighted matchings 130
6.10 The Dulmage-Mendelsohn decomposition 133
7 Local pivotal strategies for sparse matrices 137
7.1 Introduction 137
7.2 The Markowitz criterion 138
7.3 Minimum degree (Tinney scheme 2) 138
7.4 A priori column ordering 140
7.5 Simpler strategies 142
7.6 A more ambitious strategy: minimum fill-in 143
7.7 Effect of tie-breaking on the minimum degree
algorithm 145
7.8 Numerical pivoting 147
7.9 Sparsity in the right-hand side and partial solution 149
7.10 Variability-type ordering 153
7.11 The symmetric indefinite case 153
8 Ordering sparse matrices for band solution 156
8.1 Introduction 156
8.2 Band and variable-band matrices 156
8.3 Small bandwidth and profile: Cuthill-McKee
algorithm 158
8.4 Small bandwidth and profile: the starting node 162
8.5 Small bandwidth and profile: Sloan algorithm 162
8.6 Spectral ordering for small profile 163
8.7 Calculating the Fiedler vector 166
8.8 Hybrid orderings for small bandwidth and profile 167
8.9 Hager s exchange methods for profile reduction 168
8.10 Blocking the entries of a symmetric variable-band
matrix 169
8.11 Refined quotient trees 170
8.12 Incorporating numerical pivoting 173
8.12.1 The fixed bandwidth case 173
8.12.2 The variable bandwidth case 174
8.13 Conclusion 175
9 Orderings based on dissection 177
9.1 Introduction 177
9.2 One-way dissection 177
9.2.1 Finding the dissection cuts for one-way
dissection 179
9.3 Nested dissection I80
9.4 Introduction to finding dissection cuts 182
9.5 Multisection 182
9.6 Comparing nested dissection with minimum degree 185
9.7 Edge and vertex separators 186
9.8 Methods for obtaining dissection sets 188
9.8.1 Obtaining an initial separator set 188
9.8.2 Refining the separator set 189
9.9 Graph partitioning algorithms and software 191
9.10 Dissection techniques for unsymmetric systems 193
9.10.1 Background 193
9.10.2 Graphs for unsymmetric matrices 194
9.10.3 Ordering to singly bordered block diagonal
form 197
9.10.4 The performance of the ordering 200
9.11 Some concluding remarks 201
10 Implementing Gaussian elimination without symbolic
factorize 204
10.1 Introduction 204
10.2 Markowitz ANALYSE 205
10.3 FACTORIZE without pivoting 210
10.4 FACTORIZE with pivoting 213
10.5 SOLVE 215
10.6 Hyper-sparsity and linear programming 218
10.7 Switching to full form 219
10.8 Loop-free code 221
10.9 Interpretative code 222
10.10 The use of drop tolerances to preserve sparsity 225
10.11 Exploitation of parallelism 228
10.11.1 Various parallelization opportunities 228
10.11.2 Parallelizing the local ordering and sparse factorization
steps 228
11 Implementing Gaussian elimination with symbolic
FACTORIZE 232
11.1 Introduction 232
11.2 Minimum degree ordering 233
11.3 Approximate minimum degree ordering 236
11.4 Dissection orderings 238
11.5 Numerical FACTORIZE using static data structures 239
11.6 Numerical pivoting within static data structures 240
11.7 Band methods 241
11.8 Variable-band (profile) methods 244
11.9 Frontal methods: introduction 245
11.10 Frontal methods: SPD finite-element problems 246
11.11 Frontal methods: general finite-element problems 250
11.12 Frontal methods for non-element problems 251
11.13 Exploitation of parallelism 255
12 Gaussian elimination using trees 258
12.1 Introduction 258
12.2 Multifrontal methods for finite-element problems 259
12.3 Elimination and assembly trees 263
12.3.1 The elimination tree 263
12.3.2 Using the assembly tree for factorization 266
12.4 The efficient generation of elimination trees 266
12.5 Constructing the sparsity pattern of U 269
12.6 The patterns of data movement 270
12.7 Manipulations on assembly trees 271
12.7.1 Ordering of children 271
12.7.2 Tree rotations 273
12.7.3 Node amalgamation 276
12.8 Multifrontal methods: symmetric indefinite problems 277
13 Graphs for symmetric and unsymmetric matrices 281
13.1 Introduction 281
13.2 Symbolic analysis on unsymmetric systems 282
13.3 Numerical pivoting using dynamic data structures 283
13.4 Static pivoting 284
13.5 Scaling and reordering 287
13.5.1 The aims of scaling 287
13.5.2 Scaling and reordering a symmetric matrix 287
13.5.3 The effect of scaling 288
13.5.4 Discussion of scaling strategies 289
13.6 Supernodal techniques using assembly trees 290
13.7 Directed acyclic graphs 292
13.8 Parallel issues 294
13.9 Parallel factorization 295
13.9.1 Parallelization levels 295
13.9.2 The balance between tree and node parallelism 297
13.9.3 Use of memory 299
13.9.4 Static and dynamic mapping 300
13.9.5 Static mapping and scheduling 300
13.9.6 Dynamic scheduling 302
13.9.7 Codes for shared and distributed memory
computers 303
13.10 The use of low-rank matrices in the factorization 304
13.11 Using rectangular frontal matrices with local pivoting 306
13.12 Rectangular frontal matrices with structural pivoting 310
13.13 Trees for unsymmetric matrices 312
14 The SOLVE phase 315
14.1 Introduction 315
14.2 SOLVE at the node level 316
14.3 Use of the tree by the SOLVE phase 318
14.4 Sparse right-hand sides 318
14.5 Multiple right-hand sides 319
14.6 Computation of null-space basis 319
14.7 Parallelization of SOLVE 320
14.7.1 Parallelization of dense solve 321
14.7.2 Order of access to the tree nodes 321
14.7.3 Experimental results 322
15 Other sparsity-oriented issues 325
15.1 Introduction 325
15.2 The matrix modification formula 326
15.2.1 The basic formula 326
15.2.2 The stability of the matrix modification
formula 327
15.3 Applications of the matrix modification formula 328
15.3.1 Application to stability corrections 328
15.3.2 Building a large problem from subproblems 328
15.3.3 Comparison with partitioning 329
15.3.4 Application to sensitivity analysis 330
15.4 The model and the matrix 331
15.4.1 Model reduction 331
15.4.2 Model reduction with a regular submodel 333
15.5 Sparsity constrained backward error analysis 334
15.6 Why the inverse of a sparse irreducible matrix is dense 335
15.7 Computing entries of the inverse of a sparse matrix 337
15.8 Sparsity in nonlinear computations 339
15.9 Estimating a sparse Jacobian matrix 341
15.10 Updating a sparse Hessian matrix 343
15.11 Approximating a sparse matrix by a positive-definite
one 344
15.12 Solution methods based on orthogonalization 346
15.13 Hybrid methods 348
15.13.1 Domain decomposition 348
15.13.2 Block iterative methods 350
A Matrix and vector norms
B Pictures of sparse matrices
C Solutions to selected exercises
References
AUTHOR INDEX
SUBJECT INDEX
355
359
367
390
412
418
|
| any_adam_object | 1 |
| author | Duff, Iain S. Erisman, Albert M. Reid, John Ker 1938- |
| author_GND | (DE-588)129926469 |
| author_facet | Duff, Iain S. Erisman, Albert M. Reid, John Ker 1938- |
| author_role | aut aut aut |
| author_sort | Duff, Iain S. |
| author_variant | i s d is isd a m e am ame j k r jk jkr |
| building | Verbundindex |
| bvnumber | BV043868947 |
| callnumber-first | Q - Science |
| callnumber-label | QA188 |
| callnumber-raw | QA188 |
| callnumber-search | QA188 |
| callnumber-sort | QA 3188 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 |
| classification_tum | MAT 659f |
| ctrlnum | (OCoLC)973553755 (DE-599)BVBBV043868947 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02359nam a2200553 c 4500</leader><controlfield tag="001">BV043868947</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170315 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">161109s2017 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780198508380</subfield><subfield code="9">978-0-19-850838-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)973553755</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043868947</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-83</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.9/434</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 220</subfield><subfield code="0">(DE-625)143224:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 659f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65F30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65F05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Duff, Iain S.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Direct methods for sparse matrices</subfield><subfield code="c">I. S. Duff (Rutherford Appleton Laboratory, CERFACS, Toulouse, France, and Strathclyde University), A. M. Erisman (The Boeing Company, Seattle (retired) and Seattle Pacific University), J. K. Reid (Rutherford Appleton Laboratory and Cranfield University)</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Oxford University Press</subfield><subfield code="c">2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xx, 429 Seiten</subfield><subfield code="b">Illustrationen</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Numerical mathematics and scientific computation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra - Sparse matrices - Solution - Applications of computer systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sparse matrices</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Datenverarbeitung</subfield><subfield code="0">(DE-588)4011152-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Schwach besetzte Matrix</subfield><subfield code="0">(DE-588)4056053-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Schwach besetzte Matrix</subfield><subfield code="0">(DE-588)4056053-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Datenverarbeitung</subfield><subfield code="0">(DE-588)4011152-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Schwach besetzte Matrix</subfield><subfield code="0">(DE-588)4056053-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Schwach besetzte Matrix</subfield><subfield code="0">(DE-588)4056053-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Erisman, Albert M.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Reid, John Ker</subfield><subfield code="d">1938-</subfield><subfield code="0">(DE-588)129926469</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029278861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029278861</subfield></datafield></record></collection> |
| id | DE-604.BV043868947 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:37:14Z |
| institution | BVB |
| isbn | 9780198508380 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029278861 |
| oclc_num | 973553755 |
| open_access_boolean | |
| owner | DE-83 DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-83 DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 |
| physical | xx, 429 Seiten Illustrationen |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Oxford University Press |
| record_format | marc |
| series2 | Numerical mathematics and scientific computation |
| spelling | Duff, Iain S. aut Direct methods for sparse matrices I. S. Duff (Rutherford Appleton Laboratory, CERFACS, Toulouse, France, and Strathclyde University), A. M. Erisman (The Boeing Company, Seattle (retired) and Seattle Pacific University), J. K. Reid (Rutherford Appleton Laboratory and Cranfield University) Second edition Oxford Oxford University Press 2017 xx, 429 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Algebra - Sparse matrices - Solution - Applications of computer systems Datenverarbeitung Sparse matrices Data processing Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 s Datenverarbeitung (DE-588)4011152-0 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s Erisman, Albert M. aut Reid, John Ker 1938- (DE-588)129926469 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029278861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duff, Iain S. Erisman, Albert M. Reid, John Ker 1938- Direct methods for sparse matrices Algebra - Sparse matrices - Solution - Applications of computer systems Datenverarbeitung Sparse matrices Data processing Numerisches Verfahren (DE-588)4128130-5 gnd Datenverarbeitung (DE-588)4011152-0 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4011152-0 (DE-588)4056053-3 |
| title | Direct methods for sparse matrices |
| title_auth | Direct methods for sparse matrices |
| title_exact_search | Direct methods for sparse matrices |
| title_full | Direct methods for sparse matrices I. S. Duff (Rutherford Appleton Laboratory, CERFACS, Toulouse, France, and Strathclyde University), A. M. Erisman (The Boeing Company, Seattle (retired) and Seattle Pacific University), J. K. Reid (Rutherford Appleton Laboratory and Cranfield University) |
| title_fullStr | Direct methods for sparse matrices I. S. Duff (Rutherford Appleton Laboratory, CERFACS, Toulouse, France, and Strathclyde University), A. M. Erisman (The Boeing Company, Seattle (retired) and Seattle Pacific University), J. K. Reid (Rutherford Appleton Laboratory and Cranfield University) |
| title_full_unstemmed | Direct methods for sparse matrices I. S. Duff (Rutherford Appleton Laboratory, CERFACS, Toulouse, France, and Strathclyde University), A. M. Erisman (The Boeing Company, Seattle (retired) and Seattle Pacific University), J. K. Reid (Rutherford Appleton Laboratory and Cranfield University) |
| title_short | Direct methods for sparse matrices |
| title_sort | direct methods for sparse matrices |
| topic | Algebra - Sparse matrices - Solution - Applications of computer systems Datenverarbeitung Sparse matrices Data processing Numerisches Verfahren (DE-588)4128130-5 gnd Datenverarbeitung (DE-588)4011152-0 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd |
| topic_facet | Algebra - Sparse matrices - Solution - Applications of computer systems Datenverarbeitung Sparse matrices Data processing Numerisches Verfahren Schwach besetzte Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029278861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT duffiains directmethodsforsparsematrices AT erismanalbertm directmethodsforsparsematrices AT reidjohnker directmethodsforsparsematrices |