病态方程的复合结构解法

Composite structure method for ill- conditioned linear equations

为了解决病态线性方程组的求解问题 ,从结构力学角度出发 ,将病态线性方程组模型化为受力结构的平衡方程组 ,以模型结构为基础 ,推导出病态方程的复合结构解法。与常用的通过构造常微分方程组来求解病态方程的方法相比 ,该方法力学概念清楚 ,实现方法简单 ,更适合于程序化计算。该文还证明了此方法的绝对收敛性。并通过 3个数值算例与其它病态方程的求解方法的比较 ,说明该方法不但收敛速度快 ,而且精度高。

To solve the problem of ill conditioned linear equations encountered in many fields, on basis of structure mechanics, the ill conditioned linear equations were modeled as equilibrium equations of a structure subjected to incremental forces. The composite structure method (CSM) for solving ill conditioned linear equations was developed. Compared with other solution methods based on constant differential equations, the mechanical concepts behind the composite structure method are clearer. The method is easily complemented, and the absolute convergence of the CSM was also verified. Comparison of 3 numerical examples shows that the CSM is not only converges rapidly, but also more accurate.