Greedy double subspaces coordinate descent method via orthogonalization

The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively projects the estimate onto a solution space formed by two greedily selected hyperplanes via Gram-Schmidt orthogonalization. Our methods may be regarded as a simple block version of coordinate descent method which involves two active columns. The convergence analysis of this method is provided and numerical simulations also confirm the effectiveness for matrices with highly coherent columns.