Stationary Landweber method with momentum acceleration for solving least squares problems

In this article, we proposed an enhancement to the convergence rate of Landweber's method by incorporating the concept of momentum acceleration. Landweber's method is commonly used to solve least squares problems of the form min x IIAx - bII. Our approach is based on Landweber's method, which is acknowledged as a particular case of the methodologies outlined in Ding and Chen (2006). Through optimizing the momentum parameter, we were able to demonstrate the superior performance of the momentum -accelerated Landweber method. Specifically, we established that when A is a nonsquare m x n matrix with Rank( A ) = n and sigma min ( A ) not equal sigma max ( A ) , the momentum -accelerated Landweber method with the optimal parameter consistently outperforms the standard Landweber method. Our numerical experiments have confirmed the theoretical findings, demonstrating a notable improvement in the convergence rate of the Landweber method.