一种跟踪同伦曲线的自由单纯形算法

A Free-simplex Algorithm for a Kind of Tracing Homotopy Curve

给出一种新的跟踪同伦曲线的自由单纯形算法。算法的每一步都沿着同伦曲线方向构造一个单纯形，这个单纯形由某标准单纯形经正交变换得到；然后在单纯形上作线性逼近函数；最后求出线性逼近函数的解线段代替同伦曲线。如果要整个地很好地跟踪同伦曲线，还可以每步用牛顿法校正。文章最后给出一个实例。

This paper gives out a new free-simplex algorithm for tracing homotopy curve. In every algorithmic step, first, a simplex is structured along the direction of homotopy curve with the method of orthogonal transformation eo a standard simplex, then, constructing a linear approxi mation function on the simplex, and finally, its solution (a line sequment) replaces homotopy curve. newton method canbe used to correct each step in order to trace the homotopy curve well. A practical example is given at the last of the paper. 