Numerical integration on advanced computer systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1994
|
| Schriftenreihe: | Lecture notes in computer science
848 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 341 S. |
| ISBN: | 3540584102 0387584102 |
Internformat
MARC
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| 100 | 1 | |a Krommer, Arnold R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical integration on advanced computer systems |c Arnold R. Krommer ; Christoph W. Ueberhuber |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a XIII, 341 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in computer science |v 848 | |
| 650 | 7 | |a Computerwiskunde |2 gtt | |
| 650 | 4 | |a Intégration numérique - Informatique | |
| 650 | 7 | |a Intégration numérique - Informatique |2 ram | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 7 | |a algorithme intégration |2 inriac | |
| 650 | 7 | |a algorithme |2 inriac | |
| 650 | 7 | |a calcul scientifique |2 inriac | |
| 650 | 7 | |a intégration numérique |2 inriac | |
| 650 | 7 | |a logiciel mathématique |2 inriac | |
| 650 | 7 | |a parallélisme |2 inriac | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Numerical integration |x Data processing | |
| 650 | 0 | 7 | |a Parallelverarbeitung |0 (DE-588)4075860-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerische Integration |0 (DE-588)4172168-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Überhuber, Christoph W. |d 1946-2016 |e Verfasser |0 (DE-588)11800025X |4 aut | |
| 830 | 0 | |a Lecture notes in computer science |v 848 |w (DE-604)BV000000607 |9 848 | |
| 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=006543247&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006543247 | |
Datensatz im Suchindex
| _version_ | 1820874845078945792 |
|---|---|
| adam_text |
Contents
I Introduction 1
1 Applications of Numerical Integration 5
1.1 Computational Statistics 6
1.1.1 Fundamentals 6
1.1.2 Computation of Stochastic Quantities 6
1.1.3 Bayesian Statistics 8
1.2 Integral Transforms 9
1.2.1 Fundamentals 9
1.2.2 Application to Differential Equations 10
1.2.3 Finite Transforms and Fourier Series 11
1.2.4 Computational Aspects 12
1.3 Finite Element Methods 13
1.3.1 Variational Equations 13
1.3.2 Galerkin Method 15
1.3.3 Fundamentals of Finite Element Methods 16
1.4 Boundary Integral Methods 19
1.4.1 Boundary Integral Equations 19
1.4.2 Collocation Methods 21
2 Fundamentals of Numerical Integration 25
2.1 Integration Problems 25
2.2 Integration Methods 26
2.3 Conditioning of Integration Problems 30
2.4 Inherent Uncertainty of Numerical Integration 33
II Mathematical Aspects 35
3 Integrals 37
3.1 Riemann Integrals 37
3.1.1 One Dimension 37
3.1.2 Multiple Dimensions 38
3.2 Improper Integrals 39
3.2.1 One Dimensional Improper Integrals 39
x CONTENTS
3.2.2 Multi Dimensional Improper Integrals 41
3.3 Special Types of Integrals 42
3.4 Integration Regions 44
3.5 Weight Functions 45
3.6 The Preprocessing of Integrals 47
3.6.1 Transformation of Integrals 47
3.6.2 Decomposition of Integration Regions 54
3.6.3 Iteration of Integrals 55
4 Univariate Integration Formulas 57
4.1 Construction of Quadrature Formulas 57
4.1.1 Riemann Sums 57
4.1.2 Formula Construction by Approximation 60
4.1.3 Formula Construction by Acceleration 64
4.1.4 Linear Transformation of Quadrature Formulas 66
4.2 Simple Interpolatory Quadrature Formulas 67
4.2.1 Degree of Accuracy 68
4.2.2 Convergence 70
4.2.3 Closed Newton Cotes Formulas 70
4.2.4 Open Newton Cotes Formulas 73
4.2.5 Clenshaw Curtis Formulas 74
4.2.6 Gauss Formulas 75
4.2.7 Radau und Lobatto Formulas 78
4.2.8 Gauss Kronrod Formulas 78
4.3 Compound Formulas 79
4.3.1 Compound Trapezoidal Rule 82
4.3.2 IMT Formulas 84
4.4 Romberg Formulas 85
4.5 Nonlinear Extrapolation Methods 87
5 Multivariate Integration Formulas 91
5.1 Construction Principles 92
5.1.1 Riemann Sums 92
5.1.2 Construction by Approximation 92
5.1.3 Construction by Transformation 93
5.1.4 Construction by Iteration 94
5.1.5 Construction by Decomposition 97
5.2 Polynomial Rules 99
5.2.1 Multivariate Polynomials 99
5.2.2 Construction of Interpolatory Formulas 103
5.2.3 Simple Interpolatory Formulas 113
5.2.4 Compound Formulas 117
5.3 Low Discrepancy Formulas 118
5.3.1 Formula Construction by Equidistribution 118
CONTENTS xi
5.3.2 One Dimensional Low Discrepancy Sequences 124
5.3.3 Multi Dimensional Low Discrepancy Sequences 128
5.4 Pseudorandom Methods 134
5.4.1 Basic Monte Carlo Techniques 134
5.4.2 Variance Reduction Schemes 137
5.4.3 Generation of Pseudorandom Numbers 140
5.4.4 Generation of Uniform Random Numbers 141
5.4.5 Generation of Non Uniform Random Numbers 144
5.5 Lattice Rules 147
5.5.1 Formula Construction by Harmonic Analysis 147
5.5.2 Basic Definitions 149
5.5.3 Practical Representation of Lattice Rules 151
5.5.4 Error Analysis of Lattice Rules 152
5.5.5 Efficiency of Lattice Rules 159
5.6 Various Special Methods 161
III Algorithmic and Computational Aspects 163
6 Integration Algorithms 165
6.1 Error Estimation 166
6.1.1 Fundamental Uncertainty 166
6.1.2 Use of Two Integration Formulas with Different Accuracy . 167
6.1.3 Use of NuU Rules 169
6.1.4 Use of the Same Formula on Different Subdivisions 173
6.1.5 Use of Randomized Formulas 174
6.2 Sampling Strategy 176
6.2.1 Efficiency Assessment 177
6.2.2 Non Adaptive Algorithms 179
6.2.3 Adaptive Algorithms 179
6.3 Reliability Enhancement 184
6.3.1 Noise Detection 184
6.3.2 Detection of Non Integrable Functions 185
6.4 Efficiency Enhancement 187
6.4.1 Extrapolation in Non Adaptive Algorithms 187
6.4.2 Extrapolation in Adaptive Algorithms 187
6.5 Integration of Multiple Integrands 190
7 Load Distribution 193
7.1 Static Load Distribution 195
7.2 Dynamic Load Distribution 196
7.2.1 Dynamic Load Balancing Algorithms 197
7.2.2 Asynchronous Single Task Pool Methods 198
7.2.3 Synchronous Single Task Pool Methods 200
xii CONTENTS
7.2.4 Multiple Task Pool Methods 201
7.2.5 Synchronous Multiple Task Pool Methods 205
7.2.6 Asynchronous Multiple Task Pool Methods 206
7.2.7 Hierarchical Methods 209
8 Potential Parallelism in Integration Algorithms 211
8.1 Integrand Level 211
8.2 Global Extrapolation Level 214
8.3 Subdivision Level 215
8.4 Subregion Level 218
8.5 Local Extrapolation Level 219
8.6 Integration Formula Level 219
8.7 Integrand Evaluation Level 221
9 Parallelization Schemes for Integration Algorithms 223
9.1 Constituent Parts of Parallel Tasks 226
9.2 Performance Characteristics of Parallel Tasks 227
9.2.1 Algorithmic Efficiency 227
9.2.2 Degree of Parallelism 228
9.2.3 Kind of Parallelism 228
9.2.4 Predictability of Execution Times 229
9.2.5 Locality of Reference 229
10 Practical Parallelization of Integration Algorithms 233
10.1 Computer Systems for Parallel Integration 233
10.1.1 Pipelined Processors 234
10.1.2 SIMD Computers 235
10.1.3 MIMD Systems 235
10.2 Vectorization of Integration Methods 236
10.2.1 Integrand Evaluation Level 236
10.2.2 Integration Formula Level 237
10.2.3 Integrand Level 237
10.2.4 Multiple Level Vectorization 237
10.3 Parallelization of Integration Methods 238
10.3.1 Integration Formula Level 238
10.3.2 Subregion Level 239
10.3.3 Subdivision Level 240
10.3.4 Subdivision and Subregion Level 246
10.3.5 Subdivision, Subregion, and Integration Formula Level 251
10.4 Vectorization and Parallelization of Extrapolation Methods 251
10.5 Vectorization and Parallelization of Abscissa Computations 252
10.6 Vectorization and Parallelization of Reduction Operations 254
CONTENTS xiii
11 Parallel Data Management 257
11.1 Data Structures for Global Subdivision Strategies 259
11.1.1 Heaps 259
11.1.2 Other Implementations of Priority Queues 263
11.2 Concurrent Access to Data Structures 269
11.2.1 Concurrent Access to Priority Queues 270
11.2.2 New Types of Data Structures 274
IV Software Aspects 277
12 Assessment of Numerical Integration Software 279
12.1 Assessment Criteria 279
12.1.1 Reliability 280
12.1.2 Performance 282
12.1.3 Portability 283
12.2 Techniques of Assessment 285
12.2.1 Test Batteries and Performance Profiles 286
12.2.2 Fundamental Approaches to
Assessing Numerical Integration Software 290
13 Architecture Adaptive Integration Algorithms 293
13.1 Required Information 294
13.2 Practical Experience 300
Glossary of Notation 303
Bibliography 309
Authors 329
Index 334 |
| any_adam_object | 1 |
| author | Krommer, Arnold R. Überhuber, Christoph W. 1946-2016 |
| author_GND | (DE-588)11800025X |
| author_facet | Krommer, Arnold R. Überhuber, Christoph W. 1946-2016 |
| author_role | aut aut |
| author_sort | Krommer, Arnold R. |
| author_variant | a r k ar ark c w ü cw cwü |
| building | Verbundindex |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.624/0285 |
| dewey-search | 515/.624/0285 |
| dewey-sort | 3515 3624 3285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV009878714 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T15:06:12Z |
| institution | BVB |
| isbn | 3540584102 0387584102 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006543247 |
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| physical | XIII, 341 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science |
| spelling | Krommer, Arnold R. Verfasser aut Numerical integration on advanced computer systems Arnold R. Krommer ; Christoph W. Ueberhuber Berlin u.a. Springer 1994 XIII, 341 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 848 Computerwiskunde gtt Intégration numérique - Informatique Intégration numérique - Informatique ram Numerieke wiskunde gtt algorithme intégration inriac algorithme inriac calcul scientifique inriac intégration numérique inriac logiciel mathématique inriac parallélisme inriac Datenverarbeitung Numerical integration Data processing Parallelverarbeitung (DE-588)4075860-6 gnd rswk-swf Numerische Integration (DE-588)4172168-8 gnd rswk-swf Numerische Integration (DE-588)4172168-8 s DE-604 Parallelverarbeitung (DE-588)4075860-6 s Überhuber, Christoph W. 1946-2016 Verfasser (DE-588)11800025X aut Lecture notes in computer science 848 (DE-604)BV000000607 848 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006543247&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krommer, Arnold R. Überhuber, Christoph W. 1946-2016 Numerical integration on advanced computer systems Lecture notes in computer science Computerwiskunde gtt Intégration numérique - Informatique Intégration numérique - Informatique ram Numerieke wiskunde gtt algorithme intégration inriac algorithme inriac calcul scientifique inriac intégration numérique inriac logiciel mathématique inriac parallélisme inriac Datenverarbeitung Numerical integration Data processing Parallelverarbeitung (DE-588)4075860-6 gnd Numerische Integration (DE-588)4172168-8 gnd |
| subject_GND | (DE-588)4075860-6 (DE-588)4172168-8 |
| title | Numerical integration on advanced computer systems |
| title_auth | Numerical integration on advanced computer systems |
| title_exact_search | Numerical integration on advanced computer systems |
| title_full | Numerical integration on advanced computer systems Arnold R. Krommer ; Christoph W. Ueberhuber |
| title_fullStr | Numerical integration on advanced computer systems Arnold R. Krommer ; Christoph W. Ueberhuber |
| title_full_unstemmed | Numerical integration on advanced computer systems Arnold R. Krommer ; Christoph W. Ueberhuber |
| title_short | Numerical integration on advanced computer systems |
| title_sort | numerical integration on advanced computer systems |
| topic | Computerwiskunde gtt Intégration numérique - Informatique Intégration numérique - Informatique ram Numerieke wiskunde gtt algorithme intégration inriac algorithme inriac calcul scientifique inriac intégration numérique inriac logiciel mathématique inriac parallélisme inriac Datenverarbeitung Numerical integration Data processing Parallelverarbeitung (DE-588)4075860-6 gnd Numerische Integration (DE-588)4172168-8 gnd |
| topic_facet | Computerwiskunde Intégration numérique - Informatique Numerieke wiskunde algorithme intégration algorithme calcul scientifique intégration numérique logiciel mathématique parallélisme Datenverarbeitung Numerical integration Data processing Parallelverarbeitung Numerische Integration |
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