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Relative eigenvalue and singular value perturbations of scaled diagonally dominant matrices

The paper derives improved relative perturbation bounds for the eigenvalues of scaled diagonally dominant Hermitian matrices and new relative perturbation bounds for the singular values of scaled diagonally dominant square matrices. In the case of definite Hermitian matrices, the new result reduces to the existing one. In the indefinite case the new bounds are as sharp as in the definite case, although the assumptions are a bit more stringent. The result extends to some other classes of scaled diagonally dominant matrices, like skew-Hermitian and ``hidden Hermitian'' matrices. The perturbation result for the singular values enlarges the class of well-behaved matrices for accurate computation of the singular values.

Hermitian matrix ; eigenvalues ; scaled diagonally dominant matrix ; singular values ; symmetric scaling ; relative perturbations

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