多步记忆下降法求解病态线性方程组

Memory Gradient Algorithm for Solving Ill-conditioned Linear Systems

病态方程组在以传统数值算法求解过程中,因其条件数太大使算法的收敛性很差,而很难得到满意的结果。本文运用多步记忆梯度下降法给出了线性方程组的迭代求解公式;通过实例说明,无论是对称或非对称系数矩阵的病态线性方程组求解问题,在同样迭代次数的条件下,采用多步记忆梯度下降法,能得到比传统的线性迭代算法更为有效的计算结果。

It is difficult to solve the ill-conditioned linear system by using traditional algorithms, because the condition number of the system is so large. This paper tries to use the Memory Gradient Algorithm (MGA) to solve the system by giving iteration solution formula of linear system. A case study shows that MGA can obtain a better solution for symmetrical or unsymmetrical ill-conditioned linear system when the number of iteration remains constant.