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Characteristic polynomials of typical matrices are ill-conditioned
Zitatschlüssel BCC-Characteristic-Polynomials-Of-Typical-Matrices-Are-Ill-Conditioned
Autor Peter Bürgisser and Felipe Cucker and Elisa Rocha Cardozo
Jahr 2015
Monat 10
Zusammenfassung 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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