K. Yu. Osipenko

Best approximation of functions specified with an error at a finite number of points

It is proved that for convex and centrally symmetric classes of functions a linear method is included among the best (in a definite sense) methods of approximation from values specified with an error at a finite number of points. For some of the simplest classes linear best methods are constructed and their error is estimated.

Best approximation of analytic functions from information about their values at a finite number of points

For a class of bounded and analytic functions defined in a simply connected region we construct the best linear method of approximation with respect to information about the values of the function at some points of the region. We show it is unique. We obtain limiting relations for the lower bound of the norm of the error of the best method on an arbitrary compacta with connected complement where the lower bound is taken with respect to nodes from the region of analyticity.

Optimal interpolation of analytic functions

We construct an optimal interpolation formula for a particular class of analytic functions, optimization being over a set of interpolation methods which are not necessarily linear. Optimal nodes and the norm of the error are found for the optimal interpolation formula.

Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives

AbstractWe study problems of optimal recovery of functions and their derivatives in the L2 metric on the line from information about the Fourier transform of the function in question known approximately on a finite interval or on the entire line. Exact values of optimal recovery errors and closed-form expressions for optimal recovery methods are obtained. We also prove a sharp inequality for derivatives (closely related to these recovery problems), which estimates the

Optimal reconstruction of the solution of the wave equation from inaccurate initial data

k

Ismagilov type theorems for linear, Gel'fand and Bernstein n -widths

th derivative of a function in the L2-norm on the line via the L2-norm of the

How best to recover a function from its inaccurately given spectrum

n