Rational approximations to fractional powers of self-adjoint positive operators

TL;DR

This paper studies rational approximation methods for fractional powers of positive operators, providing improved error bounds and validating their effectiveness through numerical experiments.

Contribution

It introduces enhanced error bounds for rational approximations of fractional operator powers using Padé approximants, advancing previous theoretical results.

Findings

Improved error bounds for rational approximations.

Validation of approximation accuracy through numerical experiments.

Enhanced theoretical understanding of operator fractional powers.

Abstract

We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in approximation theory involving Pad\'{e} approximants. The analysis improves some existing results and the numerical experiments proves its accuracy.