USSOR迭代法收敛的一个充要条件

A necessary and sufficient condition of the USSOR iterative method

在线性方程组Ax=b的系数矩阵A为相容次序矩阵且A的Jacobi迭代矩阵的特征值μ均为纯虚数或零的条件下,得到了USSOR迭代法收敛的一个充要性定理,并给出了数值例子.

A necessary and sufficient condition for the convergence of the USSOR iterative method is given under the condition that the linear system coefficient matrix A is consistently ordered and the Eigenvalues of the Jacobi matrix of A are all pure imaginary or zero. In addition, an example is given for illustrating the results.