| Abstract: | In recent papers, some authors studied the solutions of symmetric positive definite(SPD) Toeplitz systems Tn x = b by the conjugate gradient method(CG) with different sine trans- forms based preconditioners. In this paper, we first discuss the properties of eigenvalues for the main known circulant, skew circulant and sine transform based preconditioners. A counter example shows that E.Boman's preconditioner is only positive semi-definite for the banded Toeplitz matrix. To use preconditioner effectively, then we propose a modified Boman's preconditioner and a new Cesaro sum type sine transform based preconditioner. Finally, the results of numerical experimentation with these two preconditioners are pre- sented. |
