Floating-point perturbations of Hermitian matrices

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