An iterative scheme for solving nonlinear equations with monotone operators

TL;DR

This paper introduces an iterative scheme and a Dynamical Systems Method for solving ill-posed nonlinear equations with monotone operators, providing convergence proofs, a discrepancy principle, and stopping rules.

Contribution

It presents a novel DSM algorithm with proven convergence and new stopping rules for stable solutions of ill-posed monotone operator equations.

Findings

Convergence of the proposed DSM algorithm is established.

A new discrepancy principle is introduced and justified.

A priori and a posteriori stopping rules are formulated and validated.

Abstract

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with monotone operators is proposed and its convergence is proved. A new discrepancy principle is proposed and justified. A priori and a posteriori stopping rules for the DSM algorithm are formulated and justified.