摘要
本文主要研究了带位移的反厄米特型Toeplitz线性方程组A n x=b的一个新的反厄米特循环预处理子C n,其中矩阵A n的元素是函数f(θ)=a0+ig(θ)的傅里叶系数.如果g(θ)是Wiener类实值函数,则矩阵C n非奇异;且当n足够大时,矩阵(C n-1A n)*(C n-1A n)的谱以1为聚点.数值实验进一步显示了我们的预处理子是有效的.
In this paper we propose a new skew hermitian circulant preconditioner Cn for solving skew hermitian type Toeplitz linear systems Anx = b. For a Toeplitz matrix An whoso entries are the Fourier coefficients of function f（θ） = ao ＋ ig（ θ）, where g（θ） is a real-valued function in the Wiener class, we show that Cn is nonsingular and the spec-trum of the matrix （Cn^-1An ） · （Cn^-1An ） clusters around one when n is sufficiently large. Numerical experiments fur-ther demonstrate the effectiveness of our preconditioners.
出处
《数学理论与应用》
2013年第2期29-33,共5页
Mathematical Theory and Applications
基金
Supported by the National Natural Science Foundation of China under Grant No.10771022
