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| George A., Liu J. — Computer solution of large sparse positive definite systems |
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| Предметный указатель |
Adjacency linked list 42 103
Adjacency list 41
Adjacency structure 41 46 295
Adjacent set 37
allocation see "Storage allocation"
Allocation storage 281
Ancestor 170
Arithmetic operations 13 22
Arithmetic operations, integral approximation to 14
Asymmetric block factorization 163 173 209 218
Auxiliary storage 90 226
Band 5 48 49
Band matrix 136 152
Band schemes 48 90
Bandwidth 49
Block diagonal matrix 39 245 249
Block factorization 161
Block factorization, asymmetric 163 173 209 218
Block factorization, diagonal envelope of 249
Block factorization, symmetric 166
Block fill 169
Block Gaussian elimination 169
Block solution 165
Block tridiagonal matrix 177
Bordered grid 261
Bordering method 18
Chan 91
Characteristic vector 15
Charges (computer) 287
Cholesky factor 12 16 161 172
Cholesky factorization 24
Cholesky's method 2 4 12
Chord 101
CLIQUE 38 57 157
Comparison of iterative and direct methods 11
Comparison of strategies 34
Compatible ordering 168
Component 39 105 258
Compressed storage scheme 139
Computer charges 287
Computer implementation 1
Connected component 44 71 105
Connection table 42
Cost 30 287
Cuthill — McKee ordering 58 59 76 278 see
Data structure 31 291
Degree 37
Degree update 133
Descendant 170
Diagonal block envelopes 249
Diagonal storage scheme 50
Diameter 62
Direct method 10
Disconnected graph, subgraph 40
Dissection, incomplete nested 269 275
Dissection, nested 257 259 278
Dissection, one-level 258
Dissection, one-way 227 278
Dissector 228
Distance 62
Divide and conquer 260
Dynamic storage scheme 9
Eccentricity 62
Edges 36
Eisenstat 91
Element model 157 159
Elimination graph model 93 116
Elimination graph model, explicit and implicit model 100 109
Elimination sequence 106
Envelope 48 52 57 202 249
Envelope methods 48
Envelope size 52
Envelope storage scheme 79
Envelope structure 245
execution time 34 293
experiments 277
Factorization 9 30 160
Factorization, asymmetric block 163 173 209 218
Factorization, Cholesky 24
Factorization, numerical 87 152
Factorization, symbolic 142
Factorization, symmetric block 161
Factorization, triangular 2 15
Father 170 206
Fill block 169 237
Fill-in 3 9 12 20 92 94
Filled graph 95 98 115
Filled matrix 11 92 245
Finite element, applications 277
Finite element, graph 159
Finite element, system 159
Front (wavefront) 54
Frontwidth 53 57
Full envelope 57
Gaussian elimination 2 9 11 93 169
Gibbs et al. 90
Graph model, elimination 116 124
Graph model, quotient 93 103
Graph transformation 95 108 111 131
Graph, elimination 94 99 102 106
Graph, filled 95 98 115
Graph, finite element 159
Graph, ordered 36
Graph, planar 275
Graph, quotient 105 168
Graph, section 38
Graph, star 36 55 101 113
Graph, unlabelled 37
Grid problem 227 257
Heuristic 115
i-th front 57
Identity matrix 13
Implicit model 100 109
Implicit solution 165
In-place implementation 105 109
Incomplete nested dissection 269 275
Indefinite sparse matrix 9
Indistinguishable node 122 135
Indistinguishable node with respect to elimination 119
Inner product 14 25 152
Inner product form 20 82 132
Integral approximation 14
INTERFACE 302
Irons 90
Irreducible 40
Isoparametric inequality 269
Iterative and direct methods, comparison of 11
Iterative methods 10
King ordering 78 90
Labelling 36
Leading principal submatrix 18
Leaf block 188
Level structure 178
Level structure, rooted 63
Levy 90
Linear insertion 61
Link field 42 103
Linked list, adjacency 42 103
Lower adjacency structure 46
Lower triangular 2 25 89
Markowitz scheme 115
Matrices, partitioned 160 168
Matrices, symmetric positive definite 2
Matrix product 209
Matrix, band 152 236
Matrix, block diagonal 245
Matrix, block tridiagonal 177
Matrix, filled 11 92 245
Matrix, identity 13
Matrix, indefinite 9
| Matrix, indefinite sparse 9
Matrix, modification 161 209 232
Matrix, notations 12
Matrix, permutation 9 12
Matrix, tridiagonal 23
Maximal tree partitioning 175 193
Melosh 90
mesh 159 257 278
Mesh problem 237
Minimal storage band methods 90
Minimum deficiency algorithm 157
Minimum degree algorithm 92
Minimum degree ordering 115
Model see "Elimination graph model"
Modification matrix 161 209 232
Modularity, software 10
Monotone ordering 170
Monotone profile property 57 76
Monotonely ordered tree partitioning 230
Neighborhood set 101 250
Nested dissection 278
Nested dissection ordering 257 259 278
Nested dissection, incomplete 269 275
No-cancellation assumption 27 30 92
Node, indistinguishable 122 135
Node, leaf 188
Node, peripheral 62 75
Node, pseudo-peripheral 63 67 135 238
Node, starting 59 62
Nonzero counts 13
Nonzero structure 92
Numerical experiments 277
Numerical factorization 87 152
Numerical solution 156
Numerical stability 9
Off-diagonal block 234
One-level dissection ordering 258
One-way dissection 227 278
Operations 13 22 50 54 280
Order notation 13
Order of magnitude 13
Order storage 281
Ordered graph 36
Ordering problem 5
Ordering, Cuthill — McKee 58 76
Ordering, King 78
Ordering, minimum degree 24 30 36 115
Ordering, monotone 170
Ordering, nested dissection 259
Ordering, one-level dissection 258
Ordering, quotient tree 185
Ordering, reverse Cuthill — McKee 59
Out-of-core solution 226
Outer product form 17 20 21 26 85 93
Overhead storage 31 283
overlaying 300
Partitioned matrices 160 168
Partitioning, maximal tree 175 193
Partitioning, monotonely ordered tree 230
Partitioning, quotient tree 178
Partitioning, tree 63 172 246
Path 39 96 104
Path, shortest 62
Peripheral node 62 75
Permutation matrix 9 12 115
Permutation, symmetric 4
Pivoting 9
Planar graph 275
Positive definite matrices 2 15
Primary storage 31
Principal submatrix 18
Problem, grid 227
Problem, mesh 237
Problem, ordering 5
Problem, test 1 278
Profile 48 52
Profile methods 48
Profile property, monotope 57 76
Propagation property 28 40
Pseudo-peripheral node 63 67 238
Pseudo-tridiagonal 232 236
Quotient graph 105 106 168
Quotient graph model 103 124
Quotient graph transformation 111
Quotient minimum degree algorithm 278
Quotient tree 278
Quotient tree ordering 185
Quotient tree partitioning 178
Reachable set 95 118 130 142 145 246 250
Recursive equations 260
Reducible 40
Refined quotient tree 278
reordering 4
Representative 109 110 126
Reverse Cuthill — McKee algorithm 59 69 197 278
Right hand side 2
Root 170
Rooted level structure 63
Rooted tree 170
Section graph 38
Separator 40 228 237 257 270 273
Shortest path 62
Software modularity 10
solution method 31
Solution storage 283
Solution vector 2
Son 170
span 179 191
Sparse matrix package 147
SPARSPAK 281 302
Stability, numerical 9
Star graph 55 101 102 113
Starting node 59 62
Starting vector 11
Static storage structure 9
Storage allocation 30 80 147 202
Storage scheme, diagonal 50
Storage scheme, dynamic 9
Storage scheme, envelope 79
Storage scheme, static 9
Storage, allocation 281
Storage, auxiliary 90 226
Storage, order 281
Storage, overhead 31 283
Storage, primary 31
Storage, solution 283
Subgraph 38 250
Subgrid 268
SubMatrix 18
Subtree 170
Supernode 104 110 122
Symbolic factorization 142 see
Symmetric block factorization 161
Symmetric permutation 4
Symmetric positive definite matrices 2
Test problems 1 278
Threshold value 127
Throw-away technique 256
Time, execution 34 293
Transformation, graph 95 108 131
Transformation, quotient graph 111
TRANSPOSE 2
TREE 170
Tree ordering 185
Tree partitioning 172 175 178 193 230
Tree, refined quotient 278
Triangular factorization 2 15
Triangular matrix 2 25 26 89
Triangular solution 30 165
Triangular system 3 25 82
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