engleski

On relative perturbation theory for eigenvalues and eigenvectors of block operator matrices

We are concerned with singularly perturbed spectral problems which appear in engineering sciences. Typically under the influence of a singular perturbation the model can be approximated by a simpler, perturbation independent model. Such reduced model is usually better amenable to analytic or numeric analysis. However, the question of the quality of approximation has to be answered. Frequently, correctors which yield an improved solution-capturing important phenomena which the reduced model does not see-to the original problems are required. We tackle both question for self-adjoint eigenvalue/eigenvector problems posed in a general Hilbert space. Our technique is constructive and is based on methods (relative perturbation theory) of modern Numerical Linear Algebra.

Estimation of eigenvalues ; upper and lower bounds

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