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 symmetrically scaled diagonally dominant square matrices. The perturbation result for the singular values enlarges the class of well-behaved matrices for accurate computation of the singular values.
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Matejaš, J., Hari, V. Relative eigenvalue and singular value perturbations of scaled diagonally dominant matrices . Bit Numer Math 48, 769–781 (2008). https://doi.org/10.1007/s10543-008-0200-1
- Hermitian matrix, eigenvalues, scaled diagonally dominant matrix, singular values, symmetric scaling, relative perturbations