指数为1的半正定线性系统迭代方法的收敛性

On the Convergence of Iterative Methods for Semi-Definite Linear Systems with Index One

当相容奇异线性系统系数矩阵的指数为1时,文章利用群逆的概念来介绍广义固定迭代方法半范数收敛,商收敛和收敛三者之间的关系,然后再利用群逆的概念来研究广义固定迭代方法半范数收敛的新条件.在保证迭代格式收敛的前提下,该条件比Keller的P-正则条件要弱.

We first use the group inverse to characterize the semi-norm convergence and quotient convergence the connection and distinction of stationary iterative schemes for solving consistent singular linear systems when the index of the coefficient matrix equals one. Then the new semi-norm convergent conditions of generalized iteration method are presented by using group inverse. The convergence of iterative schemes in ensuring the premise, this condition is wea- ker than Keller＇s P-regular conditions.