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

For solving large scale linear least-squares problem by iteration methods, we introduce an effective probability criterion for selecting the working columns from the coefficient matrix and construct a greedy randomized coordinate descent method. It is proved that this method converges to the unique solution of the linear least-squares problem when its coefficient matrix is of full rank, with the number of rows being no less than the number of columns. Numerical results show that the greedy randomized coordinate descent method is more efficient than the randomized coordinate descent method.