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Fast and accurate approximations to fractional powers of operators (2004.09793v1)
Published 21 Apr 2020 in math.NA and cs.NA
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.