A new double-step method for solving complex Helmholtz equation

We present a new double-step iteration method for solving the systems of linear equations that arise from finite difference discretizations of the complex Helmholtz equations. Convergence analysis of the method is discussed. An upper bound on the spectral radius of the iteration matrix of the method is presented and the parameter which minimizes this upper bound is computed. The proposed method is compared theoretically and numerically with some existing methods.