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The Theory of Cubature Formulas (Paperback, Softcover reprint of hardcover 1st ed. 1997)
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The Theory of Cubature Formulas (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Series: Mathematics and Its Applications, 415
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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.
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