摘要
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.
出处
《河北大学学报(自然科学版)》
CAS
北大核心
2005年第6期571-573,579,共4页
Journal of Hebei University(Natural Science Edition)
基金
国家自然科学基金资助项目(10071047)
关键词
PSD法
收敛
充分必要性
PSD method
convergence
necessity and sufficiency