engleski

On Ritz Approximations for Positive Definite Operators I (Theory)

We give new lower bounds on the Rayleigh--Ritz approximations of a part of the spectrum of an elliptic operator. Furthermore, we present bounds for the accompanying Ritz vectors. The bounds include a form of a relative gap between the Ritz values and the rest of the spectrum of the operator. A model example shows that the obtained bounds may be very sharp.

positive definite operators ; lower bounds ; invariant subspaces ; gap between the subspaces

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