Numerical quadrature and cubature:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Acad. Pr.
1980
|
| Series: | Computational mathematics and applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 441 S. graph. Darst. |
| ISBN: | 012238850X |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical quadrature and cubature |c H. Engels |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
List of symbols and abbreviations xi
1. Introduction
1.1 The necessity for numerical quadrature and cubature . 1
1.2 Applications of quadratures and cubatures ... 3
1.3 Historical remarks 7
1.4 Concept and aims of this book 9
1.5 General conventions 10
1.6 Remarks, problems, references 14
1.7 List of books concerning numerical quadrature and
cubature 16
2. Construction Principles for Quadrature and Cubature Formulae
2.1 Geometric constructions 18
2.2 The method of Taylor expansions 23
2.3 The method of undetermined coefficients ... 47
2.4 The method of generating functions 56
2.5 Interpolatory quadratures and cubatures .... 59
2.6 Composite rules 70
2.7 Monte Carlo and number theoretic methods ... 78
2.8 Remarks, problems, references 82
3. Error Analysis for Quadrature and Cubature Formulae
3.1 Error representations for quadratures . . . . 93
3.2 Error representation for cubature formulae by Sard
kernels 100
3.3 Determination and minimisation of error constants using
Peano and Sard kernels 108
viii Contents
3.4 Further determination and minimisation of error con¬
stants 116
3.5 Error bounds without derivatives for quadratures on
analytic function spaces 124
3.6 Error bounds without derivatives for quadratures and
cubatures on spaces of functions which are analytic in a
strip 142
3.7 Reducing errors 153
3.8 Remarks, problems, references 164
4. Convergence of Quadrature and Cubature Procedures
4.1 Definitions 170
4.2 How to prove convergence of quadrature and cubature
procedures 172
4.3 Convergence conditions for general quadrature proced¬
ures 180
4.4 Convergence conditions for cubature procedures . . . 190
4.5 Convergence for procedures consisting of composite
rules 194
4.6 Remarks, references 197
5. Orthogonal Polynomials
5.1 Definitions and properties 199
5.2 Special systems of orthogonal polynomials . . . 208
5.3 Implicitly-defined orthogonal polynomials . . . 214
5.4 Numerical calculation of the zeros of orthogonal polyno¬
mials 226
5.5 Orthogonal polynomials in the complex plane . . 237
5.6 N-Dimensional orthogonal polynomials .... 239
5.7 Applications to cubature problems 246
5.8 Remarks, problems, references 260
6. Interpolator Quadrature and Cubature Formulae - Preassigned
Nodes or Weights
6.1 Classification and general properties .... 265
6.2 The Newton-Cotes quadrature formulae .... 267
6.3 Further quadratures with equidistant nodes . . . 276
6.4 Newton-Cotes cubature formulae 277
6.5 The existence of positive cubature formulae with given
nodes 286
6.6 Equally-weighted quadrature formulae - Tschebyscheff s
problem 290
Contents ix
6.7 Equally-weighted cubature formulae .... 294
6.8 Remarks, problems, references 298
7. Refined Interpolator Quadrature
7.1 General Gauss quadratures with free nodes . . . 302
7.2 Gauss quadratures with preassigned nodes . . . 305
7.3 Classical Gauss quadratures 315
7.4 Modifications of classical Gauss quadratures having some
preassigned nodes 321
7.5 Quadratures with minimal error norm . . . . 335
7.6 Rectangle and trapezoidal rules 342
7.7 Approximate computation of indefinite integrals . . 344
7.8 Remarks, problems, references 366
8. Non-interpolatory Quadratures
8.1 Richardson extrapolation 369
8.2 Convergence of the extrapolation 375
8.3 Properties of Romberg s quadrature .... 381
8.4 Romberg cubature 391
8.5 Numerical integration of rapidly-oscillating functions . 397
8.6 Automatic integration - Adaptive methods . . . 401
8.7 Remarks, problems, references 403
9. Auxiliary Material
9.1 Bibliographic material 408
9.2 Testing quadrature subroutines 409
9.3 Some published programs 415
9.4 A list of tables 419
Author Index 429
Index of Key-words 433
Index of Programs and Tables 441
|
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| dewey-search | 515/.624 515.4/3 |
| dewey-sort | 3515 3624 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002265694 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:02Z |
| institution | BVB |
| isbn | 012238850X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488856 |
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| physical | XIV, 441 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Acad. Pr. |
| record_format | marc |
| series2 | Computational mathematics and applications |
| spelling | Engels, Hermann Verfasser aut Numerical quadrature and cubature H. Engels London [u.a.] Acad. Pr. 1980 XIV, 441 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational mathematics and applications calcul intégral inriac intégration numérique inriac polynôme orthogonal inriac quadrature numérique inriac Cubature formulas Numerical integration Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Numerische Integration (DE-588)4172168-8 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 s DE-604 Numerische Integration (DE-588)4172168-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Engels, Hermann Numerical quadrature and cubature calcul intégral inriac intégration numérique inriac polynôme orthogonal inriac quadrature numérique inriac Cubature formulas Numerical integration Integration Mathematik (DE-588)4072852-3 gnd Numerische Integration (DE-588)4172168-8 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4172168-8 |
| title | Numerical quadrature and cubature |
| title_auth | Numerical quadrature and cubature |
| title_exact_search | Numerical quadrature and cubature |
| title_full | Numerical quadrature and cubature H. Engels |
| title_fullStr | Numerical quadrature and cubature H. Engels |
| title_full_unstemmed | Numerical quadrature and cubature H. Engels |
| title_short | Numerical quadrature and cubature |
| title_sort | numerical quadrature and cubature |
| topic | calcul intégral inriac intégration numérique inriac polynôme orthogonal inriac quadrature numérique inriac Cubature formulas Numerical integration Integration Mathematik (DE-588)4072852-3 gnd Numerische Integration (DE-588)4172168-8 gnd |
| topic_facet | calcul intégral intégration numérique polynôme orthogonal quadrature numérique Cubature formulas Numerical integration Integration Mathematik Numerische Integration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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