Name
Abstract | ||
|---|---|---|
We present a new continuation algorithm to find all real solutions to a nondegenerate system of polynomial equations. Unlike homotopy methods, the algorithm is not based on a deformation of the system; instead, it traces real curves connecting the solutions to one system of equations to those of another, eventually leading to the desired real solutions. It also differs from homotopy methods in that it follows only real paths and computes no complex solutions to the original equations. The number of curves traced is essentially bounded above by the fewnomial bound for real solutions, and the method takes advantage of any slack in that bound. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s10208-011-9097-1 | Foundations of Computational Mathematics |
Keywords | Field | DocType |
Fewnomial,Khovanskii–Rolle,Gale dual,Homotopy,Continuation,Polynomial system,Numerical algebraic geometry,Real algebraic geometry,14P99,65H10,65H20 | Mathematical optimization,System of linear equations,Mathematical analysis,System of polynomial equations,n-connected,Homotopy,Homotopy analysis method,Regular homotopy,Real algebraic geometry,Homotopy lifting property,Mathematics | Journal |
Volume | Issue | ISSN |
11 | 5 | 1615-3375 |
Citations | PageRank | References |
8 | 0.79 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel J. Bates | 1 | 103 | 12.03 |
| Frank Sottile | 2 | 95 | 11.21 |