During the last two decades , homotopy continuation method has been developed to be a reliable and efficient numerical algorithm to solve such problem 同伦连续方法近20年来已经成为求解多项式系统全部孤立解的一种可靠而有效的数值算法。
It is showed that the loop space functor and the suspension functor preserve the properties of homotopy regular . and a series of homotopy equivalence spaces are constructed 摘要证明了闭路函子和同纬函子保持同伦正则性，同时构造出了一系列同伦等价的空间。
This homotopic method is an approximate analysis method , which can be more used for analyzing other behavior of the sea surface temperature anomaly of the atmosphere - ocean oscillator model 本同伦方法是近似的的解析方法，它能进一步分析海气振子的海表温度异常的其他性态。
The adaptive homotopy method uses the homotopy with parameter to get a enough good approximation xn of the genuine solution x , and then use the newton iteration to attain a more precise one 自适应延拓算法用含参同伦迭代求出一个真解x ~ *的较好近似x ~ n ，再用newton迭代精确化。
We solved multiobject nonconvex programming by means of homotopy - interior method and got the minimum weak effect solution under quasi - normal cone condition ; meanwhile we proved the convergence of this method 摘要利用同伦内点算法求解多目标非凸规划在拟锥条件下的最小弱有效解，并证明了算法的大范围收敛性。
We have derived sufficient conditions which ensure the existence of solutions of nonlinear complementarity problems , a simplicial homtopy algorithm for nonlinear complementarity problems is established 摘要在更弱的情况下，我们首先给出了非线性互补问题存在解的几个充分条件，然后给出一个求解的单纯同伦方法。
Under several suitable transformations , the problem of positive solutions for set - valued condensing mapping equation in an ordered locally convex topological space is studied by some homotopy method 摘要本文用某种同伦方法，借助于一些适当的变换，讨论了有序的局部凸拓扑线性空间中集值凝聚映象方程的正解问题。
In the course of the homotopy or the newton , the parameter will be changed when the singular case comes forth . after defining a new homotopy , the process begins with the new " homotopy - - > newton " 在同伦和newton迭代的过程中，若出现奇异，则通过非奇参数的改变，重新定义同伦，进入新一轮的“同伦newton ”迭代。
Firstly , we summarize the main methods about this kind of formulation and make some numerical simulations . secondly , we discuss the homotopy method for solving nonlinear complementarity problems 我们首先总结了这一类等价变形中的几种主要的方法，并给出了一些数值模拟实例，然后我们考虑了解决非线性互补问题的同伦方法。
Finally , we constitute a homotopy algorithm and the pass - following method for solving the differential equation in the homotopy algorithm . the example also shows the validity of our homotopy method 最后，我们建立了相应的同伦算法以及解其中微分方程初值问题的曲线跟踪法，具体的实验例子也证实了我们所提出方法的有效性。
