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The Theory of Cubature Formulas - S.L. Sobolev, Vladimir Vaskevich
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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 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. Textbooks New, Books~~Mathematics~~Counting & Numeration, Theory-of-Cubature-Formulas~~S-L-Sobolev, 999999999, The Theory of Cubature Formulas, S.L. Sobolev, Vladimir Vaskevich, 0792346319, Springer Netherlands, , , , , Springer Netherlands

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The Theory Of Cubature Formulas
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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 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. Books, Science and Geography~~Mathematics~~Calculus & Mathematical Analysis, The Theory Of Cubature Formulas~~Book~~9780792346319~~V.L. Vaskevich, S.L. Sobolev, , , , , , , , , ,, [PU: Kluwer Academic Publishers]

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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. S.L. Sobolev, Vladimir Vaskevich, Books, Science and Nature, The Theory of Cubature Formulas Books>Science and Nature, Springer Netherlands

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The Theory of Cubature Formulas
Autor:

Vaskevich, Vladimir L.; Sobolev, S. L.

Titel:

The Theory of Cubature Formulas

ISBN-Nummer:

0792346319

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.

Detailangaben zum Buch - The Theory of Cubature Formulas


EAN (ISBN-13): 9780792346319
ISBN (ISBN-10): 0792346319
Gebundene Ausgabe
Erscheinungsjahr: 1997
Herausgeber: Springer-Verlag GmbH
432 Seiten
Gewicht: 0,806 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 28.06.2007 19:32:42
Buch zuletzt gefunden am 11.12.2015 01:20:23
ISBN/EAN: 0792346319

ISBN - alternative Schreibweisen:
0-7923-4631-9, 978-0-7923-4631-9

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