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arXiv · 0709.4243

Direct and inverse theorems in the theory of approximation by the Ritz method

S. M. Torba·M. L. Gorbachuk·Ya. I. Grushka
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Abstract

For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of convergence to zero of its best approximation by exponential-type entire vectors of the operator $B$, and the $k$-modulus of continuity of the vector $x$ with respect to the operator $B$. The results are used for finding a priori estimates for the Ritz approximate solutions of operator equations in a Hilbert space.

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BibTeXRIS

S. M. Torba, M. L. Gorbachuk, Ya. I. Grushka. 2007-09-26. Direct and inverse theorems in the theory of approximation by the Ritz method. https://arxiv.org/abs/0709.4243

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