A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices
classification
🧮 math.NA
keywords
boundharmonichermitianrayleigh--ritzritzsaadvectorscondition
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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.
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