Preconditioning strategies for hermitian Toeplitz systems with nondefinite generating functions

In this paper we present new preconditioning techniques for the solution by the preconditioned conjugate gradient (PCG) method of Hermitian Toeplitz systems with real and nondefinite generating functions: actually we extend some results of Chan [IMA J. Numer. Anal., 11 (1991), pp. 333-345] and Di Benedetto, Fiorentino, and Serra [Comput. Math. Appl., 25 (1993), pp. 33-45] proved for positive definite Toeplitz systems. Moreover we demonstrate some density properties of the spectra of the preconditioned matrices. Finally, we show that the convergence speed of this PCG method is independent of the dimension of the involved matrices.