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

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. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.