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

• Datum: 2005
• Hauptverfasser: Gorbachuk, M. L., Hrushka, Ya. I., Torba, S. M., Горбачук, М. Л., Грушка, Я. І., Торба, С. М.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2005
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3629
• Назва журналу: 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...