A note on the upper bound of the spectral radius for SOR iteration matrix

Recently, Wang and Huang (J. Comput. Appl. Math. 135 (2001) 325, Corollary 4.7) established the following estimation on the upper bound of the spectral radius for successive overrelaxation (SOR) iteration matrix:ρSOR⩽1−ω+ωρGSunder the condition that the coefficient matrix A is a nonsingular M-matrix and ω⩾1, where ρSOR and ρGS are the spectral radius of SOR iteration matrix and Gauss–Seidel iteration matrix, respectively. In this note, we would like to point out that the above estimation is not valid in general.