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Characteristic polynomials of typical matrices are ill-conditioned
Citation key BCC-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.
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