English

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

Numerical Analysis 2015-12-08 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1512.01584,
  title  = {A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices},
  author = {Eugene Vecharynski},
  journal= {arXiv preprint arXiv:1512.01584},
  year   = {2015}
}