Modified Greedy Quasi Block Coordinate Descent Method for Solving Linear Least‐Squares Problems

ABSTRACT Recently, a greedy quasi‐block coordinate descent (GQBCD) method was proposed for solving overdetermined linear least‐squares problems as published in [Applied Mathematics Letters, 171(2025), 109675]. The GQBCD method is based on a random partition and the working block is determined by a greedy strategy at each step. In this paper, we introduce a modified version of the greedy quasi block coordinate descent method, referred to as MGQBCD, and provide a theoretical analysis of its convergence properties. The proposed approach enhances the original GQBCD framework by generating updated approximations through error minimization over an expanded subspace formed by two working blocks. Numerical experiments confirm both the feasibility and the improved performance of the MGQBCD method compared to the original GQBCD, particularly in terms of accuracy and convergence behavior.