A New Version of a Posteriori Choosing Regularization Parameter in Ill-Posed Problems

TL;DR

This paper introduces a new version of a posteriori parameter choice for Tikhonov regularization, providing theoretical error bounds and convergence rates, supported by a numerical example.

Contribution

It proposes a novel a posteriori regularization parameter selection method with proven error estimates and convergence analysis.

Findings

Error bounds for the regularized solution

Asymptotic convergence rate established

Numerical example demonstrating effectiveness

Abstract

The new version of a posteriori choice (NVAC) of the regularization parameter in the classical Tikhonov regularization method is considered. Lemmas and theorems on the error and the asymptotic convergence rate of the regularized solution are proved. A numerical example is given.