TY - JOUR
AU - M. L. Gorbachuk
AU - Ya. I. Hrushka
AU - S. M. Torba
PY - 2005/05/25
Y2 - 2024/05/29
TI - Direct and Inverse Theorems in the Theory of Approximation by the Ritz Method
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 57
IS - 5
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3629
AB - 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.
ER -