On eigenvalue and eigenvector estimates for nonnegative definite operators

2005/03/16 by Grubisic, Luka
#34L15 #35P15 #49R50 #65F15 #FOS: Mathematics #Numerical Analysis (math.NA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0503328

Abstract

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.

Related

• On Temple--Kato like inequalities and applications
• Sharp error bounds for Ritz vectors and approximate singular vectors
• On the Rayleigh-Ritz variational method
• Relatively bounded perturbations of J-non-negative operators
• Sharp error bounds for approximate eigenvalues and singular values from subspace methods