@article{BCC-On-The-Condition-Of-The-Zeros-Of-Characteristic-Polynomials,
Title = {On the condition of the zeros of characteristic polynomials},
Author = {Peter B\"urgisser and Felipe Cucker and Elisa Rocha Cardozo},
Pages = {72--84},
Year = {2017},
Doi = {10.1016/j.jco.2017.03.004},
Journal = {J. Complexity},
Volume = {42},
Month = {11},
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 $\Omega(n)$ (the real and imaginary parts of the entries of a Gaussian matrix are independent standard Gaussian random variables). This may provide a theoretical explanation for the common practice in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.},
Url = {http://arxiv.org/abs/1510.04419},
Url2 = {http://dx.doi.org/10.1016/j.jco.2017.03.004}
}