@unpublished{BCC-Characteristic-Polynomials-Of-Typical-Matrices-Are-Ill-Conditioned,
Title = {Characteristic polynomials of typical matrices are ill-conditioned},
Author = {Peter Bürgisser and Felipe Cucker and Elisa Rocha Cardozo},
Year = {2015},
Month = {10},
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). This gives a rigorous justification of the common wisdom in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.},
Url = {http://arxiv.org/abs/1510.04419}
}