Optimal recovery of integral operators and its applications
Vladyslav Babenko, Yuliya Babenko, Nataliia Parfinovych, Dmytro, Skorokhodov
TL;DR
This paper develops optimal methods for recovering integral operators from incomplete, error-prone data, and applies these methods to solve integral equations and boundary value problems for PDEs.
Contribution
It introduces a novel approach for the optimal recovery of integral operators and derives error bounds for solutions to related integral and differential equations.
Findings
Optimal recovery methods minimize error in integral operator estimation.
Derived explicit error bounds for solutions to integral equations.
Applied recovery techniques to boundary and initial value problems for PDEs.
Abstract
In this paper we present the solution to the problem of recovering rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE's.
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Taxonomy
TopicsNumerical methods in inverse problems · Mathematical Analysis and Transform Methods · Mathematical functions and polynomials