A modified T. Chanʹs preconditioner for Toeplitz systemsI

We present a modified T. Chanʹs preconditioner for solving Toeplitz linear systems by the preconditioned conjugate gradient (PCG) method in this paper. Especially, we give some results when the matrices are Hermitian positive definite Toeplitz matrices. The operation and convergence of the PCG method are discussed. Numerical examples presented illus- trate the effectiveness of the preconditioner obtained.