Comments on “Symmetric successive overrelaxation methods for rank deficient linear systems”: [Applied Mathematics and Computation 173 (2006) 404–420]

摘要

In this note, we present a critical review on the paper “Symmetric successive overrelaxation methods for rank deficient linear systems” by authors Darvishi and Khosro-Aghdam [M.T. Darvishi, R. Khosro-Aghdam, Symmetric successive overrelaxation methods for rank deficient linear systems, Appl. Math. Comput. 173 (2006) 404–420]. We point out that a sufficient condition for the semiconvergence of SSOR iteration matrix, one of the main results in their paper, is not true and its proof is unacceptable. In fact, this problem has been thoroughly solved and one nice set of necessary and sufficient conditions has been given out by us, see [B. Zheng, K. Wang,Symmetric successive overrelaxation methods for solving the rank deficient linear least squares problem, Appl. Math. Comput. 169 (2005) 1305–1323].