Dynamical systems method for solving linear finite-rank operator equations

TL;DR

This paper develops a Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems, providing theoretical justification for stopping rules and constructing an iterative scheme to improve solution stability.

Contribution

It introduces a novel DSM-based iterative scheme with proven stopping rules for effectively solving ill-conditioned linear systems.

Findings

Justified a priori and a posteriori stopping rules

Constructed an iterative scheme for ill-conditioned systems

Enhanced stability and convergence of solutions

Abstract

A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An {\it a priori} and {\it a posteriori} stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.