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

  • M. L. Gorbachuk
  • Ya. I. Hrushka Iн-т математики НАН України, Київ
  • S. M. Torba

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.
Published
25.05.2005
How to Cite
GorbachukM. L., HrushkaY. I., and TorbaS. M. “Direct and Inverse Theorems in the Theory of Approximation by the Ritz Method”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 5, May 2005, pp. 633–643, https://umj.imath.kiev.ua/index.php/umj/article/view/3629.
Section
Research articles