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.
Fast and accurate approximations to fractional powers of operators
Novati, Paolo
2021-01-01
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.File in questo prodotto:
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