The minimum value function for the Tikhonov regularization and its applications

TL;DR

This paper studies the properties of the minimum value function in Tikhonov regularization, proposing an efficient method and new criterion for selecting the regularization parameter to improve solution accuracy.

Contribution

It introduces a detailed analysis of the minimum value function and presents novel methods for optimal regularization parameter determination in Tikhonov regularization.

Findings

Properties of the minimum value function are characterized.

An efficient method for parameter selection is proposed.

A new criterion for regularization parameter determination is introduced.

Abstract

The minimum value function appearing in Tikhonov regularization technique is very useful in determining the regularization parameter, both theoretically and numerically. In this paper, we discuss the properties of the minimum value function. We also propose an efficient method to determine the regularization parameter. A new criterion for the determination of the regularization parameter is also discussed.