Improvements to Solving Polynomial Systems:  Optimal Linear Product Start Systems and More

Methods to decrease the number of paths tracked in homotopy continuation methods are highly desirable.  In general, as the complexity of the construction of a start systems increases, the number of starting paths decreases.  Finding a balance between this reduction in the starting solutions and the complexity of their construction is a nontrivial task.  In this talk, I will give an algorithm on how we can obtain an optimal linear product start system, and the implications this has for improving solving polynomial systems.