Dynamical Systems Gradient method for solving nonlinear equations with monotone operators

TL;DR

This paper introduces a Dynamical Systems Gradient method for solving ill-posed nonlinear equations with monotone operators, proposing a new stopping rule validated through numerical experiments, demonstrating its efficiency.

Contribution

The paper develops a new stopping rule for the Dynamical Systems Gradient method applied to monotone operator equations, with theoretical justification and empirical validation.

Findings

The new stopping rule is effective and efficient.

Numerical experiments confirm the method's practical performance.

Abstract

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many applications.