A new free-parameter double splitting iteration method for PDE-constrained optimization problems

Abstract

We present a new free-parameter double splitting iteration method for solving the system of linear equations arisen from finite element discretization of a PDE-constrained optimization problem. We prove that the eigenvalues of the iteration matrix of the method are included in the interval (0,12]. So the spectral radius of the iteration matrix is less than or equal to 12, which shows that the method is unconditionally convergent. Numerical comparison with two known methods is given to show the effectiveness of the method.