On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems

Abstract

The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods.