实对称正定Toeplitz矩阵的带位移的Sine预处理子

The Shifted Sine Preconditioner for Real Symmetric Positive Definite Toeplitz Matrices

本文研究了求解实对称正定Toeplitz线性方程组的预处理共轭梯度法.基于实对称Toeplitz矩阵都有一个三角变换分裂(TTS)的事实,我们提出了带位移的Sine预处理子TS,分析了预处理矩阵的谱性质,并讨论了每步迭代的计算复杂度.数值实验表明该预处理子比T.Chan预处理子^([2])更有效.

This paper studies the solution of real symmetric positive definite Toeplitz matrices by the precondi- tioned conjugate gradient method. Based on the fact that the real symmetric Toeplitz matrix admits a triangular transform splitting （TTS）, we propose the shifted Sine preconditioner Ts, the spectral properties of the pre- conditioned matrix are analyzed, and the arithmetic complexity is discussed. The numerical experiments show that our preconditioner is more effective than T. Chan＇s preconditioner.