On eigenvalue and eigenvector estimates for nonnegative definite operators

Details On eigenvalue and eigenvector estimates for nonnegative definite operators On eigenvalue and eigenvector estimates for nonnegative definite operators

2005-03-16

arxiv.org/abs/math/0503328v1

Mathematics

Spectral Theory

28 pages and 1 figure

Scientific paper

In this article we further develop a perturbation approach to the Rayleigh--Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of the theory to nonnegative definite operators . The perturbation argument enables us to solve two problems in one go: We determine which part of the spectrum of the operator is being approximated by the Ritz values and compute the approximation estimates. We also present a Temple--Kato like inequality which --unlike the original Temple--Kato inequality-- applies to any test vectors from the quadratic form domain of the operator.

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