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Perturbed Regeneration for Finding All Isolated Solutions of Polynomial Systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bates, Daniel J. Davis, Brent R. Eklund, David Hanson, Eric M. Peterson, Chris |
| Copyright Year | 2013 |
| Abstract | Given a polynomial system f : C N ! C n , the methods of numerical algebraic geometry produce numerical approximations of the isolated solutions of f(z) = 0, as well as points on any positive-dimensional components of the solution set, V(f). One of the most recent advances in this eld is regeneration, an equation-by-equation solver that is often more ecient than other methods. However, the basic form of regeneration will not necessarily nd all isolated singular solutions of a polynomial system. In this article, we describe a technique for using regeneration to nd all isolated solutions of a polynomial system, including all isolated singular solutions. This technique also yields the multiplicity of each isolated solution. This method { perturbed regeneration { slightly decreases the eciency of regeneration while increasing its applicability. This two-part method consists of computing the solution of a perturbed problem via regeneration, followed by a generally inexpensive parameter homotopy to the target system f(z). This article describes the use of this method to nd all isolated solutions and briey investigates the eect of this sort of perturbation on problems having positive-dimensional solution sets. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.colostate.edu/~bates/preprints/perturbed_regen.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
