On a sequence of points of interest for numerical quadrature

Abstract

(where XI I), X\2) •• • ,xIS) are the S coo rdinates of the point X i), we call R the "error" of the quadrature form ula (1). R depends on the integrand f and on the se t of points XI, ... ,XN; for R to be r ela ti vely small for som e wide class of functions th e se t of points s hould be, in so me se nse, we ll distributed in the cube Cs . An appropriate se nse of " we ll di st ributed" is that , for a regio n A in Cs , the numbe r of points of th e se t which li e in A s hould be approximately N times the volume of A. Restric ting attention to regions which are inte rval s with one vertex at th e origin-i.e. , which are of th e form