Preconditioning Research For Solving Ill Conditioned Toeplitz Systems

Toeplitz systems have a rich background,which arise widely form many application areas,such as scientific computing,information theory and engineering.Due to its general ill-conditioning properties,it is critical to design efficient preconditioners to improve the efficiency of the related solution algorithms,so that we can solve these problems effectively.On the basis of the construction ideas of several efficient preconditioners,a class of new preconditioners are proposed,which are applicable for both the Hermitian and the non-Hermitian ill-conditioned Toeplitz systems.In addition,spectral distributions of the preconditioned matrices are analyzed based on the Courant-Fischer minimax theorem,and the convergence properties of the corresponding Krylov space methods are studied.Finally,numerical experiments are presented to verify the feasibility and effectiveness of the constructed preconditioners for solving both the Hermitian and the non-Hermitian Toeplitz systems.