English

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 Ω(n){\Omega}(n). 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}
}
R2 v1 2026-06-22T11:20:58.099Z