Details:
Title  Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets  Author(s)  Andrew J. Sommese, Jan Verschelde  Type  Article in Journal  Abstract  Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for fourbar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A procedure of A. Sommese and C. Wampler consists in slicing the components with linear subspaces in general position to obtain generic points of the components as the isolated solutions of an auxiliary system. Since this requires the solution of a number of larger overdetermined systems, the procedure is computationally expensive and also wasteful because many solution paths diverge. In this article an embedding of the original polynomial system is presented, which leads to a sequence of homotopies, with solution paths leading to generic points of all components as the isolated solutions of an auxiliary system. The new procedure significantly reduces the number of paths to solutions that need to be followed. This approach has been implemented and applied to various polynomial systems, such as the cyclic nroots problem.  Keywords  polynomial system, numerical homotopy continuation, components of solutions, numerical algebraic geometry, generic points, embedding  Length  31  Copyright  Academic Press 
File 
 URL 
dx.doi.org/10.1006/jcom.2000.0554 
Language  English  Journal  Journal of Complexity  Volume  16  Number  3  Pages  572602  Year  2000  Month  September  Translation 
No  Refereed 
No 
