Gauss–Seidel method with oblique direction

In this paper, a Gauss–Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to system of linear equations, where coefficient matrix may be full rank or deficient and overdetermined underdetermined. Through method, number iteration steps running time can reduced greater extent find solution, especially when columns A are close correlation. It theoretically proved that GSO converges solution. At same time, randomized version–randomized (RGSO) established, its convergence proved. Theoretical proof numerical results show RGSO more efficient than coordinate descent (CD) (RCD) method.