Abstract
In this paper, we look at a particular case of application which is Hölder continuous, namely the map from a matrix A to one of its eigenvalues λ, when it is multiple defective. Two asymptotic Hölder condition numbers are considered: one (with respect to the other) is associated with a generalization of the Fréchet (with respect to Gateaux) derivative [A. Harrabi, About Hölder condition numbers of Gateaux and Fréchet type for general nonlinear functions, Manuscript — CERFACS, 1998]. We illustrate on a fully developed 3×3 example why these asymptotic condition numbers may not be appropriate for analyzing eigencomputations performed in finite precision. We present the complementary view point of differential geometry, developed by A. Ilahi in [A. Ilahi, Validation du calcul sur ordinateur: application de la théorie des singularités, Ph.D. Thesis, Université des Sciences Sociales, Toulouse I, 1998], which is based on the stratification diagram in C 3×3 . The distance to the stratum indicates when this complementary viewpoint is required.
Published Version
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