Информационная система "Конференции"

Abstracts

Approximation of functions and quadrature formulas

A lattice rule is a cubature formula which employ abscissas that lie on an $n$-dimensional lattice. A cubature formula of trigonometric degree $d$ is one that integrates exactly all trigonometric monomials $$ phi_alpha(x_1,dots,x_n)=e^{2pi i(alpha_1x_1+ldots+alpha_nx_n)} $$ of degree $leq d$. Construction of such cubature formulas is quite simple, but increase of values $d$ and $n$ results in useful increase of computation time. Other way to create cubature formulas of high trigonometric degree uses conception of series of lattice rules $$ intlimits_0^1dotsintlimits_0^1f(x_1,dots,x_n),dx_1 dots dx_n approx frac{1}{N}sumlimits_{j=1}^N f left(left{frac{p_1 j}{N}right},dots, left{frac{p_n j}{N}right}right). $$ Series of lattice rules with parameters $p_i=p_i(k)$ ($1 leq i leq n$) and $N=N(k)$ (where $k$ is parameter of series) gives a method allows to create cubature formula of trigonometric degree $d(k)$. In this paper we describe several methods of series construction and results of theirs use.

Note. Abstracts are published in author's edition

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