On optimal recovery of unbounded operators from inaccurate data

TL;DR

This paper investigates the optimal methods for recovering unbounded operators from inaccurate data, demonstrating that truncation methods achieve optimal accuracy under certain conditions, with applications to numerical differentiation and parabolic equations.

Contribution

It establishes the optimality of truncation methods for recovering unbounded operators and applies these results to specific problems like numerical differentiation.

Findings

Truncation methods achieve optimal recovery accuracy.

Optimal recovery is characterized by minimal data and maximal precision.

Applications include numerical differentiation and backward parabolic equations.

Abstract

The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain conditions are met, realizes the optimal values of the studied quantities. As an illustration of the general results, problems of numerical differentiation and the backward parabolic equation are considered.