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

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

2007-09-26

arxiv.org/abs/0709.4243v1

M. L. Horbachuk, Ya. I. Hrushka, and S. M. Torba, "Direct and inverse theorems in the theory of approximation by the Ritz meth

Mathematics

Functional Analysis

10 pages

Scientific paper

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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