On the condition of characteristic polynomials
Numerical Analysis
2015-11-24 v2
Abstract
We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is . This may provide an explanation for the common wisdom in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.
Keywords
Cite
@article{arxiv.1510.04419,
title = {On the condition of characteristic polynomials},
author = {Peter Buergisser and Felipe Cucker and Elisa Rocha Cardozo},
journal= {arXiv preprint arXiv:1510.04419},
year = {2015}
}