A Maximal Residual Two Subspace Projection Algorithm for Solving Least-Squares Problems

doi:10.1007/s42967-025-00495-1

Abstract

Abstract: We study a greedy coordinate descent method to solve large linear least-squares problems expanding on a randomized coordinate descent method presented by Leventhal and Lewis (Math. Oper. Res. 35: 641-654, 2010). For an overdetermined system, they proved its exponential convergence, regardless of its consistency. In our work, we study a greedy selection rule for the coordinate descent method which we refer to as the two-dimensional maximal residual Gauss-Seidel (D2MRGS) method. In this method, we select two coordinates in every iteration and treat the current approximation in those directions. Convergence is analyzed for the stated method and numerical experiments are provided to demonstrate its efficiency.

Key words: Coordinate descent, Iterative techniques, Least-squares problem, Petrov-Galerkin condition, Projection methods, Randomized methods

CLC Number:

Ashif Mustafa, Manideepa Saha. A Maximal Residual Two Subspace Projection Algorithm for Solving Least-Squares Problems[J]. Communications on Applied Mathematics and Computation, 2026, 8(3): 1226-1242.

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