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＜電子ブック＞
The Theory of Cubature Formulas / by S.L. Sobolev, Vladimir L. Vaskevich
(Mathematics and Its Applications ; 415)

版	1st ed. 1997.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1997
本文言語	英語
大きさ	XXII, 418 p. 1 illus : online resource
著者標目	*Sobolev, S.L author Vaskevich, Vladimir L author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Approximation theory LCSH:Functional analysis LCSH:Functions of real variables FREE:Computational Mathematics and Numerical Analysis FREE:Approximations and Expansions FREE:Functional Analysis FREE:Real Functions
一般注記	1. Problems and Results of the Theory of Cubature Formulas -- 2. Cubature Formulas of Finite Order -- 3. Formulas with Regular Boundary Layer for Rational Polyhedra -- 4. The Rate of Convergence of Cubature Formulas -- 5. Cubature Formulas with Regular Boundary Layer -- 6. Universal Asymptotic Optimality -- 7. Cubature Formulas of Infinite Order -- 8. Functions of a Discrete Variable -- 9. Optimal Formulas -- References -- Notation Index 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 HTTP:URL=https://doi.org/10.1007/978-94-015-8913-0

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