A note on the improving modified Gauss–Seidel (IMGS) method

In this paper, we first provide another proof for a theorem given by Sun (L. Sun, A comparison theorem for the SOR iterative method, J. Comput. Appl. Math. 181 (2005) 336–341) by showing that spectral radius of the Gauss–Seidel method is not greater than that of the SOR(ω) method when 0 < ω ⩽ 1. Next, convergence results of the IMGS method for both an H-matrix and a symmetric positive definite matrix are provided.