Backward Error Measures for Roots of Polynomials
Numerical Analysis
2020-03-24 v1 Numerical Analysis
Abstract
We analyze different measures for the backward error of a set of numerical approximations for the roots of a polynomial. We focus mainly on the element-wise mixed backward error introduced by Mastronardi and Van Dooren, and the tropical backward error introduced by Tisseur and Van Barel. We show that these measures are equivalent under suitable assumptions. We also show relations between these measures and the classical element-wise and norm-wise backward error measures.
Cite
@article{arxiv.2003.09618,
title = {Backward Error Measures for Roots of Polynomials},
author = {Simon Telen and Sascha Timme and Marc Van Barel},
journal= {arXiv preprint arXiv:2003.09618},
year = {2020}
}
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20 pages