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On the condition of the zeros of characteristic polynomials
Citation key BCC-On-The-Condition-Of-The-Zeros-Of-Characteristic-Polynomials
Author Peter Bürgisser 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 $Ømega(n)$ (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.
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