Majorization bounds for Ritz values of self-adjoint matrices
Functional Analysis
2020-07-10 v2 Numerical Analysis
Numerical Analysis
Abstract
A priori, a posteriori, and mixed type upper bounds for the absolute change in Ritz values of self-adjoint matrices in terms of submajorization relations are obtained. Some of our results prove recent conjectures by Knyazev, Argentati, and Zhu, which extend several known results for one dimensional subspaces to arbitrary subspaces. In addition, we improve Nakatsukasa's version of the theorem of Davis and Kahan. As a consequence, we obtain new quadratic a posteriori bounds for the absolute change in Ritz values.
Keywords
Cite
@article{arxiv.1905.06998,
title = {Majorization bounds for Ritz values of self-adjoint matrices},
author = {Pedro Massey and Demetrio Stojanoff and Sebastian Zarate},
journal= {arXiv preprint arXiv:1905.06998},
year = {2020}
}
Comments
20 pages. This is the version of the paper which appears in SIMAX, with minor changes (one of them in the title of the paper)