Interpolatory quadrature formulas for meromorphic integrandsy

Abstract

Let I W ( f ) = R b a f ( x ) W ( x ) dx , where the integrand f is analytic on [ a; b ] and probably meromorphic on an open set V [ a; b ]. A variety of Gauss quadrature formulas based on rational functions, have been intensively applied in the last thirty years to evaluate I W ( f ). One of the drawbacks of these procedures is that to become efficient, coefficients and nodes must depend on the poles of f . Monegato [8] presented a less costly approach based on interpolatory rules whose nodes are those common to a couple of simultaneous quadrature formulas of polynomial type. In this paper we examine a variant of Monegato's method, to estimate I W ( f ) by means of procedures which are not of Gauss type. Our approach is mainly based upon the rational modiffication BW=A , which is superior to W=A , when some zeros of f lie near [ a; b ]