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中文摘要：
半迭代法或称Chebyshev半迭代法是解线性方程组的一个常用且比较有效的方法,它大大提高了矩阵的收敛速度.本文依据Varga,Young,胡家赣书中介绍的迭代矩阵为对称阵时,半迭代法的收敛性的理论,以Chebyshev多项式及其基本性质作为基本工具,对一类反对称迭代矩阵,研究其半迭代法的收敛情况.从而为扩大半迭代法的适用范围奠定了基础.
英文摘要：
Semi-iterative Method is a normal and effective method of solving the linear algebra equation. It can often achieve a large improvement of the convergence. Convergence of semi-iterative method was discussed by Vatga, Young and HU Jia-gan when iterative matrix is symmetric. In this paper, using Chebyshev polynomial and its properties, we obtain the convergence of semi-iterative method for a class of antisymmetric iterative matrix. Thus we extend the usual convergence condition to a new situation.
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