Note to the mixed-type splitting iterative method for \(Z\)-matrices linear systems (Q939500)

The authors propose a mixed-type splitting iterative method, using an auxiliary nonnegative diagonal matrix and an auxiliary strictly lower triangular matrix, for solving linear systems, where the coefficient matrix is a Z-matrix. Additionally, they prove that the rate of convergence of the mixed-type iterative method is faster than that of the successive overrelaxation and the accelerated overrelaxation iterative methods. Numerical results are presented to illustrate the effectiveness of the proposed method.