The theory of cubature formulas:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht <<[u.a.]>>
Kluwer Acad. Publ.
1997
|
| Series: | Mathematics and its applications
415 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XXI, 416 S. |
| ISBN: | 0792346319 |
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MARC
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| 100 | 1 | |a Sobolev, S. L. |d 1908-1989 |e Verfasser |0 (DE-588)119002833 |4 aut | |
| 245 | 1 | 0 | |a The theory of cubature formulas |c by S. L. Sobolev and V. L. Vaskevich |
| 264 | 1 | |a Dordrecht <<[u.a.]>> |b Kluwer Acad. Publ. |c 1997 | |
| 300 | |a XXI, 416 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 415 | |
| 500 | |a Aus dem Russ. übers. | ||
| 700 | 1 | |a Vaskevič, Vladimir L. |e Sonstige |4 oth | |
| 830 | 0 | |a Mathematics and its applications |v 415 |w (DE-604)BV008163334 |9 415 | |
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Record in the Search Index
| _version_ | 1804140396280807424 |
|---|---|
| adam_text | Contents
Foreword to the English Translation ix
Preface xi
From the Preface to Introduction to the Theory of Cubature
Formulas xix
Chapter 1. Problems and Results of the Theory of Cubature
Formulas 1
§ 1. Exact Formulas 1
§ 2. Functional-Analytical Statement of the Problem 7
§ 3. The Order of a Cubature Formula on Infinitely Differentiable
Functions 20
§ 4. Errors in W2(m) 23
§ 5. Expansion of the L,™ * Norm of an Error with Arbitrary Nodes 33
§ 6. The Weights of Optimal Cubature Formulas on a Given Lattice 37
Chapter 2. Cubature Formulas of Finite Order 43
§ 1. Formulas of Interpolatory Type 43
§ 2. Rotation Invariant Cubature Formulas 47
§ 3. Rotation Invariant Cubature Formulas on the Sphere in R3 64
vi Contents
Chapter 3. Formulas with Regular Boundary Layer for Rational
Polyhedra 74
§ 1. Rational Polyhedra 75
§ 2. Constructing Formulas for Rational Polyhedra 82
§ 3. A Formal Boundary Layer 86
Chapter 4. The Rate of Convergence of Cubature Formulas 93
§ 1. A Universal Lower Bound on the Rate of Convergence 93
§ 2. The Rate of Convergence of a Homogeneous Error 103
§ 3. The Bakhvalov Theorem 117
§ 4. The Rate of Convergence of an Equidistributed Error 122
Chapter 5. Cubature Formulas with Regular Boundary Layer 131
§ 1. The Properties of the Extremal Function of an £2 -Optimal
Error 131
§ 2. Errors in the Xj (n) Space of Compactly-Supported Functions 142
§ 3. Constructing a Formula with Regular Boundary Layer 148
§ 4. Asymptotic Expansion of the Norm of an Error with Regular
Boundary Layer 154
§ 5. The Properties of the Extremal Function of an Error in Ij™ O,) 164
Chapter 6. Universal Asymptotic Optimality 173
§ 1. Cubature Formulas with Bounded Boundary Layer
in Hilbert Spaces 173
§ 2. Cubature Formulas with Bounded Boundary Layer
in Holder Spaces- 200
§ 3. Constructing Universal Asymptotically Optimal Formulas 211
Contents vii
Chapter 7. Cubature Formulas of Infinite Order 221
§ 1. Weak Convergence of Cubature Formulas 221
§ 2. The Function Classes H(x, A, A) and C(x, A, A) 230
§ 3. The Properties of H(x, A) and C(x, A) for x 1 235
§ 4. The Function Classes ty(p, a,fj.) 239
§ 5. The Classes of Periodic Functions H(x, A, ) 245
§ 6. Convergence of Cubature Formulas in H(x, A,X) 253
§ 7. Gevrey Classes of Functions in a Single Independent Variable .. 257
§ 8. Convergence of Euler-Maclaurin and Gregory Quadrature Formulas
on Gevrey Classes 270
§ 9. The Sequence of the Fourier Coefficients of an Error 275
§ 10. The Fourier Transform of a Local Error 280
§ 11. The Norm of the Error of a Gregory Quadrature Formula .... 288
Chapter 8. Functions of a Discrete Variable 292
§ 1. Operations over Discrete Functions 292
§ 2. Spaces of Discrete Functions 312
§ 3. The Fourier Transform of a Discrete Function 324
Chapter 9. Optimal Formulas 331
§ 1. Statement of the Problem of Optimal Weights 331
§ 2. The Fundamental Solution to the Convolution Equation 337
§ 3. A Discrete Analog of the Polyharmonic Operator 344
§ 4. The Weights of Optimal Formulas and the Extension Problem 351
§ 5. A One-Dimensional Discrete Analog of a Derivative of Even
Order 355
§ 6. The Roots of the Euler Polynomial 361
§ 7. The First Asymptotic Formula 368
§ 8. The Weights of Optimal Quadrature Formulas 375
References 389
Notation Index 411
Subject Index 413
|
| any_adam_object | 1 |
| author | Sobolev, S. L. 1908-1989 |
| author_GND | (DE-588)119002833 |
| author_facet | Sobolev, S. L. 1908-1989 |
| author_role | aut |
| author_sort | Sobolev, S. L. 1908-1989 |
| author_variant | s l s sl sls |
| building | Verbundindex |
| bvnumber | BV024423953 |
| ctrlnum | (OCoLC)613019781 (DE-599)BVBBV024423953 |
| dewey-full | 515.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.43 |
| dewey-search | 515.43 |
| dewey-sort | 3515.43 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024423953 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:59:19Z |
| institution | BVB |
| isbn | 0792346319 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018401400 |
| oclc_num | 613019781 |
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| owner | DE-83 DE-188 |
| owner_facet | DE-83 DE-188 |
| physical | XXI, 416 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Sobolev, S. L. 1908-1989 Verfasser (DE-588)119002833 aut The theory of cubature formulas by S. L. Sobolev and V. L. Vaskevich Dordrecht <<[u.a.]>> Kluwer Acad. Publ. 1997 XXI, 416 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 415 Aus dem Russ. übers. Vaskevič, Vladimir L. Sonstige oth Mathematics and its applications 415 (DE-604)BV008163334 415 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018401400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sobolev, S. L. 1908-1989 The theory of cubature formulas Mathematics and its applications |
| title | The theory of cubature formulas |
| title_auth | The theory of cubature formulas |
| title_exact_search | The theory of cubature formulas |
| title_full | The theory of cubature formulas by S. L. Sobolev and V. L. Vaskevich |
| title_fullStr | The theory of cubature formulas by S. L. Sobolev and V. L. Vaskevich |
| title_full_unstemmed | The theory of cubature formulas by S. L. Sobolev and V. L. Vaskevich |
| title_short | The theory of cubature formulas |
| title_sort | the theory of cubature formulas |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018401400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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