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A generalization of Saad’s bound on harmonic Ritz vectors of Hermitian matrices. (English) Zbl 1382.65106

Summary: We prove a Saad’s type bound for harmonic Ritz vectors of a Hermitian matrix. The new bound reveals a dependence of the harmonic Rayleigh-Ritz procedure on the condition number of a shifted problem operator. Several practical implications are discussed. In particular, the bound motivates incorporation of preconditioning into the harmonic Rayleigh-Ritz scheme.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15B57 Hermitian, skew-Hermitian, and related matrices

Software:

JDQZ; FEAST; lobpcg.m
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Full Text: DOI arXiv

References:

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