Abstract

NUMERICAL EXPERIMENTS ON TOEPLITZ SYSTEMS OF LINEAR EQUATIONS USING THE PRECONDITIONED CONJUGATE GRADIENT METHOD

1C. C. Jibunoh (Jnr) and 2M.N.O Ikhile

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Abstract In this paper, we consider the conjugate gradient and the preconditioned conjugate gradient algorithms for solving Symmetric Positive Definite (SPD) Toeplitz systems. From these we develop what is defined as the Ci preconditioners which are modifications of the Ku and Kuo preconditioners. The Ci preconditioners are designed to speed up the iterative process in the earilier algorithms so as to obtain faster convergence. These Ci preconditioners also work satisfactorily for both the well and ill-conditioned Toeplitz systems and in many cases demonstrate superiority over the Strang and T.Chan?s preconditioners. Keywords: Symmetric Positive Definite (SPD), Conjugate Gradient (CG), Preconditioned Conjugate Gradient (PCG), Krylov space, Matlab codes.

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