Abstract
We study a reliable pole selection for the rational approximation of the resolvent of fractional powers of operators in both the finite and infinite dimensional setting. The analysis exploits the representation in terms of hypergeometric functions of the error of the Padé approximation of the fractional power. We provide quantitatively accurate error estimates that can be used fruitfully for practical computations. We present some numerical examples to corroborate the theoretical results. The behavior of rational Krylov methods based on this theory is also presented.
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This work was funded by GNCS-INdAM, PRA-University of Pisa and FRA-University of Trieste. The authors are members of the INdAM research group GNCS.
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Aceto, L., Novati, P. Padé-type Approximations to the Resolvent of Fractional Powers of Operators. J Sci Comput 83, 13 (2020). https://doi.org/10.1007/s10915-020-01198-w
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DOI: https://doi.org/10.1007/s10915-020-01198-w