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Field name	Details
Dewey Class	518
Title	The Theory of Cubature Formulas ([EBook]) / by S. L. Sobolev, V. L. Vaskevich.
Author	Sobolev, Sergei L'vovich , 1908-1989
Added Personal Name	Vaskevich, Vladimir L. author.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1997.
Physical Details	XXII, 418 pages : 1 illus. : online resource.
Series	Mathematics and its applications ; 415
ISBN	9789401589130
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-015-8913-0
Links to Related Works	Subject References: Approximation theory . Approximations and Expansions . Computational Mathematics and Numerical Analysis . Computer mathematics . Functional Analysis . Functions of real variables . Mathematics . Real Functions . Authors: author . Sobolev, Sergei L'vovich 1908-1989 . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications . Classification: 518 .

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The Theory of Cubature Formulas

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