9804846 Li Sparse polynomial systems occur frequently in a wide variety of applications in sciences and engineering where the knowledge of all their isolated solutions is essential. Practical evidence has shown that homotopy continuation algorithms are efficient, reliable and accurate in finding all the isolated zeros of polynomial systems. Moreover, the method is inherently parallel and is therefore a natural candidate for distributed processing architectures. The proposed research is to be directed along several avenues in solving polynomial systems by the newly emerged polyhedral homotopies. The essence of the project is to develop efficient computational algorithms, which involves a theoretical study of the method, investigation of the stability and efficiency of the algorithm, and benchmark testing for a wide range of problems. The ultimate goal of the project is to produce a high-quality software package that can be used to solve large-scale real world applications on a wide variety of advanced architectures.
