Construction of the optimal set of quadrature rules in the sense of Borges

Abstract

Abstract. In this paper we give a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges [Numer. Math., 67 (1994), pp. 271–288] for definite integrals with the same integrand and interval of integration but with different weight functions related to an arbitrary multi-index. We present a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges for four weight functions and explain how to perform an analogous construction for an arbitrary number of weight functions.