Fast and accurate approximations to fractional powers of operators

Abstract

Abstract In this paper we consider some rational approximations to the fractional powers of self-adjoint positive operators, arising from the Gauss–Laguerre rules. We derive practical error estimates that can be used to select a priori the number of Laguerre points necessary to achieve a given accuracy. We also present some numerical experiments to show the effectiveness of our approaches and the reliability of the estimates.