A polynomial homotopy is a family of polynomial systems in one parameter, which defines solution paths starting from known solutions and ending at solutions of a system that has to be solved. We consider paths leading to isolated singular solutions, to which the Taylor series converges logarithmically. Whether or not extrapolation algorithms manage to accelerate the slowly converging series depends on the proximity of poles close to the disk of convergence of the Taylor series.

翻译：多项式同伦是含单参数的多项式系统族，其定义从已知解出发、终止于待解系统解的求解路径。考虑通向孤立奇异解的路径，此类路径的泰勒级数以对数方式收敛。外推算法能否加速缓慢收敛的级数，取决于极点与泰勒级数收敛圆盘的接近程度。