RELATIVE RESIDUAL BOUNDS FOR EIGENVALUES OF HERMITIAN MATRICES.

This paper presents a linear and quadratic residual bound for eigenvalues of an indefinite possible singular Hermitian matrix. These bounds are a generalization of results on a semidefinite Hermitian matrix [Z. Drmač and V. Hari, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 21–29]. The bounds here contain an extra factor which depends on the norm of a J-unitary matrix, where J is diagonal matrix with ±1 on its diagonal. [ABSTRACT FROM AUTHOR]