Erratum to: “A note on the preconditioned Gauss–Seidel method for -matrices” [J. Comput. Appl. Math. 219 (1) (2008) 59–71]

In this note, some errors in a recent article by Niki et al. [H. Niki, T. Kohno, M. Morimoto, The preconditioned Gauss–Seidel method faster than the SOR method, J. Comput. Appl. Math. 219 (2008) 59–71] are pointed out and a new proof for the corresponding result is presented.