Author/Authors :
In this paper، نويسنده , , we look at a particular case of application which is H?lder continuous، نويسنده , , namely the map from a matrix A to one of its eigenvalues ?، نويسنده , , when it is multiple defective. Two asymptotic H?lder 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، نويسنده , , About H?lder condition numbers of Gateaux and Fréchet type for general nonlinear functions، نويسنده , , Manuscript — CERFACS، نويسنده , , 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، نويسنده , , developed by A. Ilahi in [A. Ilahi، نويسنده , , Validation du calcul sur ordinateur: application de la théorie des singularités، نويسنده , , Ph.D. Thesis، نويسنده , , Université des Sciences Sociales، نويسنده , , Toulouse I، نويسنده , , 1998]، نويسنده , , which is based on the stratification diagram in C3×3. The distance to the stratum indicates when this complementary viewpoint is required.، نويسنده ,
Keywords :
Index , H?lder condition number , Fréchet and Gateaux derivatives , Exact arithmetic , Finite precision arithmetic , Stratification associated with the commutator AX?XA , Multiple defective eigenvalue
