A circulant-matrix-based new accelerated GSOR preconditioned method for block two-by-two linear systems from image restoration problems

Abstract In this paper, we construct a circulant-matrix-based new accelerated GSOR (CNAGSOR) iteration method for a class of large and sparse block two-by-two linear systems of generalized saddle-point structure. Theoretical results about the convergence properties and eigenvalues distribution of the preconditioning matrix are studied in detail. Implementations in the image restoration problem and in the PDE-constraint optimization problem are made to verify the feasibility and the efficiency of the new methods.