A necessary and sufficient condition for semiconvergence and optimal parameter of the SSOR method for solving the rank deficient linear least squares problem

Let A∈Crm×n be partitioned asA=A11A12A21A22,whereA11∈Crr×r.Write B=A21A11-1 and C=A11-1A12. Suppose that B ≠ 0. For finding the minimum norm least squares solution A+b of the linear systemsAx=b,many authors studied the SOR, AOR, and SSOR methods for solving the augmented systems(1.1)A^z=bˆ,and obtained many results. In this paper we deeply study the SSOR method, whose iteration matrix is written as Jω, and prove the following new conclusions: