A Gaussian method for the operator square root
Numerical Analysis
2022-02-04 v1 Numerical Analysis
Abstract
We consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. The approximation is of rational type and comes from the use of the Gauss-Legendre rule applied to a special integral formulation of the problem. We derive sharp error estimates, based on the use of the numerical range, and provide some numerical experiments. For practical purposes, the finite dimensional case is also considered. In this setting, the convergence is shown to be of exponential type.
Cite
@article{arxiv.2202.01622,
title = {A Gaussian method for the operator square root},
author = {Eleonora Denich and Paolo Novati},
journal= {arXiv preprint arXiv:2202.01622},
year = {2022}
}