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Floatingpoint perturbations of Hermitian matrices
, 1995
"... We consider the perturbation properties of the eigensolution of Hermitian matrices. For the matrix entries and the eigenvalues we use the realistic "floatingpoint" error measure jffia=aj. Recently, Demmel and Veseli'c considered the same problem for a positive definite matrix H sh ..."
Abstract

Cited by 26 (13 self)
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We consider the perturbation properties of the eigensolution of Hermitian matrices. For the matrix entries and the eigenvalues we use the realistic "floatingpoint" error measure jffia=aj. Recently, Demmel and Veseli'c considered the same problem for a positive definite matrix H showing that the floatingpoint 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 wellbehaved 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 normestimates for the perturbations of the eigenprojections, and show that some of our techniques extend to nonhermitian matrices. However, unlike in the positive definite case, we are still unable to simply descr...