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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 onthe condition number of a shifted problem operator. Several practicalimplications are discussed. In particular, the bound motivates incorporation ofpreconditioning into the harmonic Rayleigh--Ritz scheme.

A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices