A note on SOR(ω) splitting of an M-matrix

摘要

Recently, Wang and Huang (J. Comput. Appl. Math. 135 (2001) 325, Corollary 4.7) assumed that SOR(ω) splitting with ω⩾1 is a weak regular splitting of an M-matrix. In this note, we point out that SOR(ω) splitting with ω>1 can never be a weak regular splitting of an M-matrix. This shows that Chang's counterexample (J. Comput. Appl. Math. 167 (2004) 251, Example 1) is not an appropriate one since the SOR(ω) splitting with ω>1 given there is not a weak regular splitting.