Abstract
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: ρ SOR ⩽1−ω+ωρ GS under the condition that the coefficient matrix A is a nonsingular M-matrix and ω⩾1, where ρ SOR and ρ GS 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.
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