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A Gauss-Laguerre approach for the resolvent of fractional powers

    Eleonora Denich, Laura Grazia Dolce, Paolo Novati

ETNA - Electronic Transactions on Numerical Analysis, pp. 517-537, 2023/08/21

doi: 10.1553/etna_vol58s517

doi: 10.1553/etna_vol58s517


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doi:10.1553/etna_vol58s517



doi:10.1553/etna_vol58s517

Abstract

This paper introduces a very fast method for the computation of the resolvent of fractional powers of operators. The analysis is kept in the continuous setting of (potentially unbounded) self-adjoint positive operators in Hilbert spaces. The method is based on the Gauss-Laguerre rule, exploiting a particular integral representation of the resolvent. We provide sharp error estimates that can be used to a priori select the number of nodes to achieve a prescribed tolerance.

Keywords: resolvent of fractional powers, Gauss-Laguerre rule, functions of operators