Chebyshev polynomial acceleration for block SOR methods for solving the rank-deficient least-squares problem

In this article, we give the acceleration of the block successive overrelaxation (SOR) method for solving the rank-deficient least-squares problem. Santos and Silva proposed the two-block SOR method and the three-block SOR method. Here, we consider the acceleration of the two-block SOR method and the three-block SOR method using the Chebyshev polynomial and derive what we term the C-2-block SOR method and the C-3-block SOR method. The advantage of our methods is that we can get good results with very small iteration number. The comparison between the C-2-block method and the C-3-block method is presented. Finally, numerical examples are given.