PSD迭代方法收敛的一个充分必要条件

A Necessary and Sufficient Condition for the Convergence of a PSD Iterative Method

在线性方程组系数矩阵A为(1，1)相容次序矩阵及A的Jacobi迭代矩阵的特征根μj2<1的条件下，得出了PSD迭代法收敛的一个充分必要条件，并给出了SSOR，JOR，PJ等迭代法收敛的充分必要条件．最后根据定理确定实例的收敛区间．

A necessary and sufficient condition for the convergence of a PSD iterative method is given under the condition that the coefficient matrix A is consistently ordered and the eigenvalues of the Jacobi matrix of A are all real. For SSOR, JOR, PJ iterative methods, the range of convergence are also given under the same condition, In addition, an example is given for illustrating the results.