摘要
本文介绍了能可靠求得多项式方程组全部解的连续法。首先阐述了连续法求解多项式方程组的基本原理;然后研究了多项式方程组同伦路径的特点及同伦路径的跟踪方法,并以此为基础构造了具体算法;最后介绍了同伦路径跟踪中减少发散路径的齐次化方法。本文工作为连续法在各应用学科中进一步推广应用奠定了基础。
Continuation method for finding all solutions to polynomial equations is introduced. The basic theory and the latest achievement are discussed in detail. This paper makes it easy for finding all solutions to polynomial equations and lays a foundation for using continuation method in other applied sciences.
