一种病态线性系统求解的新算法

A new algorithm for solving ill-conditioned linear systems

本文提出了一种病态线性系统求解的新算法,该算法将原线性系统求解的问题转化为极小值点的最优化问题,借助不对分寻优法进行迭代求解,并结合引入的伪误差来解决当方程组阶数非常大时出现的误差积累问题。文末算例实验表明,本文算法对于良态线性系统、病态线性系统均有较好的求解效果。该算法为病态线性系统利用计算机迭代求解提供了直接的参考方法。

The paper proposes a new algorithm for solving ill-conditioned linear systems.The algorithm changes the ill-conditioned linear systems into the extremum optimization problems. Based on non-half 2 division optimization method and the false error introduced, the error accumulation problem can be solved. In the final part of this paper ,the experiments show that this algorithm has good results for normal linear systems and ill-conditioned ones. The algorithm provides a reference method for computer program iterative procedure for ill conditioned linear systems.