New estimates for Ritz vectors

  title={New estimates for Ritz vectors},
  author={Andrew Knyazev},
  journal={Math. Comput.},
The following estimate for the Rayleigh–Ritz method is proved: |λ̃− λ||(ũ, u)| ≤ ‖Aũ− λ̃ũ‖ sin∠{u; Ũ}, ‖u‖ = 1. Here A is a bounded self-adjoint operator in a real Hilbert/euclidian space, {λ, u} one of its eigenpairs, Ũ a trial subspace for the Rayleigh–Ritz method, and {λ̃, ũ} a Ritz pair. This inequality makes it possible to analyze the fine structure of the error of the Rayleigh–Ritz method, in particular, it shows that |(ũ, u)| ≤ C 2, if an eigenvector u is close to the trial subspace with… CONTINUE READING
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