2017
Том 69
№ 6

# Direct and Inverse Theorems in the Theory of Approximation by the Ritz Method

Abstract

For an arbitrary self-adjoint operator B in a Hilbert space $\mathfrak{H}$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in \mathfrak{H}$ 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.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 5, pp 751-764.

Citation Example: Gorbachuk M. L., Hrushka Ya. I., Torba S. M. Direct and Inverse Theorems in the Theory of Approximation by the Ritz Method // Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 633–643.

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