m-step preconditioners for nonhermitian positive definite Toeplitz systems

Abstract

It is known that if A is a Toeplitz matrix，then A enjoys a circulant and skew circulant splitting(de— noted by CSCS)，i．e．，A=C+ S with C a circulant matrix and S a skew circulant matrix． Based on the CSCS iteration，we give m-step preconditioners P for certain classes of Toeplitz matrices in this paper．We show that if both C and S are positive definite，then the spectrum of the preconditioned matrix(PA)^* PA are clustered around one for some moderate size ． Experimental results show that the proposed preconditioners perform slightly better than T．Chan’S preconditioners for some moderate size m．