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

• Date: 2005
• Main Authors: Gorbachuk, M. L., Hrushka, Ya. I., Torba, S. M., Горбачук, М. Л., Грушка, Я. І., Торба, С. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3629
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 approxima...