Name
Abstract | ||
|---|---|---|
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing computations on an adaptively chosen affine coordinate patch. Second, for parameterized systems which are overdetermined, we investigate options for adaptively selecting a well-constrained subsystem to restore numerical stability. Finally, since one is typically interested in only computing real solutions for parameterized problems which arise from applications, we investigate a scheme for heuristically identifying solution paths which appear to be ending at nonreal solutions and truncating them. We demonstrate these three aspects on two problems arising in computer vision. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.amc.2018.03.028 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Numerical algebraic geometry,Homotopy continuation,Parameter homotopy,Overdetermined system,Algebraic vision | Affine transformation,Heuristic,Overdetermined system,Mathematical optimization,Parameterized complexity,System of polynomial equations,Homotopy analysis method,Mathematics,Numerical stability,Computation | Journal |
Volume | ISSN | Citations |
332 | 0096-3003 | 2 |
PageRank | References | Authors |
0.36 | 9 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan D. Hauenstein | 1 | 269 | 37.65 |
| Margaret H. Regan | 2 | 2 | 2.39 |