Ritz value bounds that exploit quasi-sparsity

Abstract. Absolute and relative perturbation bounds for Ritz values of complex square matrices are presented. The bounds exploit quasi-sparsity of the eigenvectors, apply to specified eigenvalues, and do not use the entire matrix. The bounds are tighter than existing bounds when eigenvectors are quasi-sparse. The bounds are customized for Hermitian banded and tridiagonal matrices. A bound for the (relative) accuracy of the relative Ritz value separation is also derived.

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