基于DIXON结式的聚筛法的自动化软件GAS

The Automatic Software GAS of Gather-and-Sift Based on DIXON Resultant

非线性代数方程组的求解是一个尚未完全解决的问题。基于DIXON结式的聚筛法是求解非线性代数方程组的一种非常有效的方法,然而运用该算法的求解过程需要进行专家干预,使得该方法不能被广泛地推广和应用。对基于DIXON结式的聚筛法进行了深入地分析和研究,针对聚筛法在不能从DIXON导出方程组DPS中直接选出关于所有变元的三角列的情况下效率较低的问题,在计算机编程算法方面提出了变元轮换法和方程扩充法,使得该问题得到了有效地解决。在此改进的基础上开发的自动化软件GAS在非线性代数方程组的求解方面有很高的效率,整个计算过程无需人工介入,从而解决了该方法仅仅停留在理论研究领域而不能应用于实际工程计算的问题。

The solving of nonlinear algebraic equation system still needs further study. Gather-and-Sift based on DIXON resultant is an effective algorithm for solving nonlinear algebraic equation system. This algorithm is not applied widely because it requires interacting of the expert. The author studies this algorithm and makes two improvements on programming skills in order to solve the problem of lower efficiency when the middle results of DPS are not satisfied. The author develops an automatic software, GAS, by applying the skills. GAS has higher efficiency in solving nonlinear algebraic equation system without any interacting in the whole processing and can be used in real engineering computing.