Naslov
Floating-point perturbations of Hermitian matrices

Autori
Veselić, Krešimir ; Slapničar, Ivan

Izvornik
Linear algebra and its applications (0024-3795) 195 (1993); 81-116

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Sažetak
We consider the perturbation properties of the eigensolution of Hermitian matrices. For the matrix entries and the eigenvalues we use the realistic "floating-point" error measure |\delta a/a|. Recently, Demmel and Veselić considered the same problem for a positive definite matrix H, showing that the floating-point perturbation theory holds with constants depending on the condition number of the matrix A=DHD, where A_{ii}=1 and D is a diagonal scaling. We study the general Hermitian case along the same lines, thus obtaining new classes of well-behaved matrices and matrix pairs. Our theory is applicable to the already known class of scaled diagonally dominant matrices as well as to matrices given by factors - like those in symmetric indefinite decompositions. We also obtain norm estimates for the perturbations of the eigenprojections, and show that some of our techniques extend to non-Hermitian matrices. However, unlike in the positive definite case, we are still unable to describe simply the set of all well-behaved Hermitian matrices.

Izvorni jezik
Engleski

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