The computational complexity of differential and integral equations: an information-based approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford u.a.
Oxford Univ. Press
1991
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| Series: | Oxford mathematical monographs
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | IX, 331 S. |
| ISBN: | 0198535899 9780198535898 |
Staff View
MARC
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| 100 | 1 | |a Werschulz, Arthur G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The computational complexity of differential and integral equations |b an information-based approach |c Arthur G. Werschulz |
| 264 | 1 | |a Oxford u.a. |b Oxford Univ. Press |c 1991 | |
| 300 | |a IX, 331 S. | ||
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| 650 | 4 | |a Computational complexity | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
2 Example: a two point boundary value problem 6
2.1 Introduction 6
2.1.1 Problem formulation 7
2.1.2 Information 8
2.1.3 Model of computation 8
2.2 Error, cost, and complexity 9
2.3 A minimal error algorithm 10
2.4 Complexity bounds 14
2.5 Comparison with the finite element method 16
2.6 Standard information 20
2.7 Final remarks 22
3 General formulation 23
3.1 Introduction 23
3.2 Problem formulation 24
3.3 Information 24
3.4 Model of computation 26
3.5 Algorithms, their errors, and their costs 27
3.6 Complexity 29
3.7 Randomized setting 30
3.8 Asymptotic setting 31
4 The worst case setting: general results 32
4.1 Introduction 32
4.2 Radius and diameter 33
4.3 Complexity 35
4.4 Linear problems 37
4.4.1 Definition 37
4.4.2 Adaptive vs. nonadaptive information 38
4.4.3 Optimal information 39
4.4.4 Linear algorithms for linear problems 43
viii Contents
4.4.5 Complexity 48
4.5 The residual error criterion 50
4.5.1 Basic definitions 50
4.5.2 Reduction to the approximation problem 52
4.5.3 Linear algorithms 53
4.5.4 Complexity 58
5 Elliptic partial differential equations in the worst case setting 61
5.1 Introduction 61
5.2 Variational elliptic boundary value problems 63
5.3 Problem formulation 71
5.4 The normed case with arbitrary linear information 73
5.5 The normed case with standard information 98
5.6 The seminormed case 111
5.7 Can adaption ever help? 124
6 Other problems in the worst case setting 146
6.1 Introduction 146
6.2 Linear elliptic systems 147
6.2.1 Problem formulation 148
6.2.2 Arbitrary linear information 152
6.2.3 Standard information 162
6.3 Fredholm problems of the second kind 170
6.3.1 Problem formulation 171
6.3.2 Arbitrary linear information 174
6.3.3 Standard information 185
6.4 Ill posed problems 196
6.4.1 Definition 197
6.4.2 The absolute error criterion 199
6.4.3 The residual error criterion 206
6.5 Ordinary differential equations 227
6.5.1 Standard information 228
6.5.2 Other information 230
7 The average case setting 233
7.1 Introduction 233
7.2 Some basic measure theory 234
7.3 General results for the average case setting 237
7.4 Complexity of shift invariant problems 245
7.4.1 Problem definition 245
7.4.2 Continuous linear information 251
Contents ix
7.4.3 Standard information 264
7.5 Ill posed problems 272
7.5.1 The absolute error criterion 273
7.5.2 The residual error criterion 279
7.6 The probabilistic setting 283
7.6.1 General results 284
7.6.2 Results for shift invariant problems 288
7.6.3 Ill posed problems 292
8 Complexity in the asymptotic and randomized settings 293
8.1 Introduction 293
8.2 Asymptotic setting 294
8.3 Randomized setting 298
Appendix 303
A.I Introduction 303
A.2 Sobolev spaces 303
A.2.1 Definition 303
A.2.2 Some useful results and inequalities 305
A.2.3 Interpolation by polynomials 307
A.3 Weakly coercive linear equations 309
Bibliography 314
Author index 323
Subject index 326
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:16:49Z |
| institution | BVB |
| isbn | 0198535899 9780198535898 |
| language | English |
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| physical | IX, 331 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Werschulz, Arthur G. Verfasser aut The computational complexity of differential and integral equations an information-based approach Arthur G. Werschulz Oxford u.a. Oxford Univ. Press 1991 IX, 331 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Hier auch später erschienene, unveränderte Nachdrucke Complexité de calcul (Informatique) ram Equations différentielles - Solutions numériques ram Equations intégrales - Solutions numériques ram complexité calcul inriac solution numérique inriac équation différentielle inriac équation intégrale inriac Computational complexity Differential equations Numerical solutions Integral equations Numerical solutions Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Berechnungskomplexität (DE-588)4134751-1 s DE-604 Integralgleichung (DE-588)4027229-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002909095&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Werschulz, Arthur G. The computational complexity of differential and integral equations an information-based approach Complexité de calcul (Informatique) ram Equations différentielles - Solutions numériques ram Equations intégrales - Solutions numériques ram complexité calcul inriac solution numérique inriac équation différentielle inriac équation intégrale inriac Computational complexity Differential equations Numerical solutions Integral equations Numerical solutions Berechnungskomplexität (DE-588)4134751-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4134751-1 (DE-588)4012249-9 (DE-588)4027229-1 |
| title | The computational complexity of differential and integral equations an information-based approach |
| title_auth | The computational complexity of differential and integral equations an information-based approach |
| title_exact_search | The computational complexity of differential and integral equations an information-based approach |
| title_full | The computational complexity of differential and integral equations an information-based approach Arthur G. Werschulz |
| title_fullStr | The computational complexity of differential and integral equations an information-based approach Arthur G. Werschulz |
| title_full_unstemmed | The computational complexity of differential and integral equations an information-based approach Arthur G. Werschulz |
| title_short | The computational complexity of differential and integral equations |
| title_sort | the computational complexity of differential and integral equations an information based approach |
| title_sub | an information-based approach |
| topic | Complexité de calcul (Informatique) ram Equations différentielles - Solutions numériques ram Equations intégrales - Solutions numériques ram complexité calcul inriac solution numérique inriac équation différentielle inriac équation intégrale inriac Computational complexity Differential equations Numerical solutions Integral equations Numerical solutions Berechnungskomplexität (DE-588)4134751-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Complexité de calcul (Informatique) Equations différentielles - Solutions numériques Equations intégrales - Solutions numériques complexité calcul solution numérique équation différentielle équation intégrale Computational complexity Differential equations Numerical solutions Integral equations Numerical solutions Berechnungskomplexität Differentialgleichung Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002909095&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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