A Krylov subspace method for the approximation of bivariate matrix functions
Numerical Analysis
2018-02-22 v2 Operator Algebras
Abstract
Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fr\'echet derivative. In this work, we propose a novel tensorized Krylov subspace method for approximating such bivariate matrix functions and analyze its convergence. While this method is already known for some instances, our analysis appears to result in new convergence estimates and insights for all but one instance, Sylvester matrix equations.
Cite
@article{arxiv.1802.05759,
title = {A Krylov subspace method for the approximation of bivariate matrix functions},
author = {Daniel Kressner},
journal= {arXiv preprint arXiv:1802.05759},
year = {2018}
}
Comments
Revised version contains polynomial approximation results for phi function in appendix