The Theory of Cubature Formulas:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
415 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated. Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics |
| Beschreibung: | 1 Online-Ressource (XXII, 418 p) |
| ISBN: | 9789401589130 9789048148752 |
| DOI: | 10.1007/978-94-015-8913-0 |
Internformat
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| 245 | 1 | 0 | |a The Theory of Cubature Formulas |c by S. L. Sobolev, V. L. Vaskevich |
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| 300 | |a 1 Online-Ressource (XXII, 418 p) | ||
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| 490 | 0 | |a Mathematics and Its Applications |v 415 | |
| 500 | |a This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated. Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Computer science / Mathematics | |
| 650 | 4 | |a Computational Mathematics and Numerical Analysis | |
| 650 | 4 | |a Approximations and Expansions | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Real Functions | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Vaskevich, V. L. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804153100633636864 |
|---|---|
| any_adam_object | |
| 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 | BV042424103 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864065571 (DE-599)BVBBV042424103 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8913-0 |
| format | Electronic eBook |
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| id | DE-604.BV042424103 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401589130 9789048148752 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859520 |
| oclc_num | 864065571 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XXII, 418 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer Netherlands |
| record_format | marc |
| 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, V. L. Vaskevich Dordrecht Springer Netherlands 1997 1 Online-Ressource (XXII, 418 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 415 This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated. Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics Mathematics Functional analysis Computer science / Mathematics Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Real Functions Informatik Mathematik Vaskevich, V. L. Sonstige oth https://doi.org/10.1007/978-94-015-8913-0 Verlag Volltext |
| spellingShingle | Sobolev, S. L. 1908-1989 The Theory of Cubature Formulas Mathematics Functional analysis Computer science / Mathematics Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Real Functions Informatik Mathematik |
| 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, V. L. Vaskevich |
| title_fullStr | The Theory of Cubature Formulas by S. L. Sobolev, V. L. Vaskevich |
| title_full_unstemmed | The Theory of Cubature Formulas by S. L. Sobolev, V. L. Vaskevich |
| title_short | The Theory of Cubature Formulas |
| title_sort | the theory of cubature formulas |
| topic | Mathematics Functional analysis Computer science / Mathematics Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Real Functions Informatik Mathematik |
| topic_facet | Mathematics Functional analysis Computer science / Mathematics Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Real Functions Informatik Mathematik |
| url | https://doi.org/10.1007/978-94-015-8913-0 |
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