构建复杂Dixon矩阵递归算法的改进

Improving the recursive algorithm to construct complicated Dixon matrices

针对多于5个变元的复杂多项式系统的Dixon矩阵的构建问题,基于递归算法提出了一种改进算法.采用动态规划的思想,自下而上地构建Dixon矩阵,避免了Dixon多项式的重复计算,并给出了使用该算法计算Dixon矩阵的具体实例.该算法与递归算法一样,可以在同样的计算平台上处理其他方法所不能解决的一些复杂多项式系统求解问题,但与递归算法相比,减少了须要计算的Dixon多项式的数量,提高了计算效率.

Based on existing recursive algorithm, an improved algorithm was proposed to construct the Dixon matrices. The improved algorithm used the dynamic programming ideas. The Dixon matrices were built by the algorithm from the bottom up. It avoided computing the Dixon polynomials repeat- edly, and the sample that a Dixon matrix was calculated using the improved algorithm was given. The improved algorithm can solve some problems that cannot be tackled by other methods on the same computer platform for some complicated polynomial systems as the recursive algorithm. Compared with the recursive algorithm, the improved algorithm reduces the number of Dixon polynomials that need to be calculated, and it improves the computational efficiency.