预处理子为(I+S′)的Gauss-Seidel迭代法的收敛定理

A Convergence Theorem for the Gauss-Seidel Iterative Method with the Preconditioner (I+S′)

1991年,Gunawardrnna等人提出了预处理子为(I+S)的改进的Gauss-Seidel方法.我们在本文中用预处理子(I+S′)代替(I+S),这里 i=1,2,…,n-1,j=i+1,(S′)ij=-ai,ki0 其它,证明了这种改进的Gauss-Seidel迭代法也是收敛的.

In 1991,Gunawardena et al have reported the modified Gauss-Seidel method with a preconditoner (I+S).In this paper, we propose to use a preconditioner (I+S′) instead of (I+S).Here(S′)_(ij)=-a_(i,k_i)i=1,2,...,n-1,j=i+1, 0otherwise, We get the convergence theorem for the proposed method.