A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices
arXiv:1512.015844 citationsh-index: 12
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Theoretical advance for numerical linear algebra, providing insight into harmonic Rayleigh-Ritz procedure, but incremental as it extends existing bounds.
The authors prove a Saad-type bound for harmonic Ritz vectors of Hermitian matrices, revealing dependence on the condition number of a shifted operator, and discuss implications including motivation for preconditioning.
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.