Showing papers by "Jilin University published in 1962"
2 citations
TL;DR: In this article, a numerical integration procedure with the best possible degree of approximation for a class of non-periodic functions is proposed, which is based on the idea of NIKOLS integration.
Abstract: This paper is concerned with a kind of numerical integration procedure with the best possible degree of approximation for a class of non-periodic functions. The basic idea is actually derived from some preliminary work of S. M. NIKOLS~:I [9]; and our results are as sharp as those obtained by I. F. SHARYGI• [10] by using the analytic number-theoretic method. Let U(0=< xl=< t . . . . . 0<= xs<= t) be the unit hypercube of s-dimensional space in which X=-(x l , . . . , xs) denotes a typical point vector. Denote by W ('/(M; U) a function class, {/(X)}, of which eve ry / (X) =~/(x 1 . . . . . xs) possesses r-th partial derivatives O'[/~x'~ which are piecewise continuous with respect to each of the variables and uniformly bounded on U, viz.