Characteristic polynomials and pseudospectra
نویسنده
چکیده
In this paper, we study the ε-lemniscate of the characteristic polynomial in relation to the pseudospectrum of the associated matrix. It is natural to investigate this question because these two sets can be seen as generalizations of eigenvalues. The question of numerical determination of the ε-lemniscate raises the problem of computing the characteristic polynomial p. We can express the coefficients of the characteristic polynomial in the power basis: we use a formation of a Krylov sequence. In order to investigate the practical determination of the characteristic polynomial, we propose a detailed study of its backward error. keywords : pseudospectrum, characteristic polynomial, rounding error, backward error, ε-lemniscate.
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