Name
Title | ||
|---|---|---|
Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces. |
Abstract | ||
|---|---|---|
Bertini_real is a compiled command line program for numerically decomposing the real portion of a positive-dimensional complex component of an algebraic set. The software uses homotopy continuation to solve a series of systems via regeneration from a witness set to compute a cell decomposition. The implemented decomposition algorithms are similar to the well-known cylindrical algebraic decomposition (CAD) first established by Collins in that they produce a set of connected cells. In contrast to the CAD, Bertini_real produces cells with midpoints connected to boundary points by homotopies, which can easily be numerically tracked. Furthermore, the implemented decomposition for surfaces naturally yields a triangulation. This CAD-like decomposition captures the topological information and permits further computation on the real sets, such as sampling, visualization, and three-dimensional printing. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1145/3056528 | ACM Trans. Math. Softw. |
Keywords | Field | DocType |
Solvers,Nonlinear Equations,Computations on Polynomials,Numerical algebraic geometry,homotopy continuation,polynomial system,real solutions,cell decompositions | Mathematical optimization,Midpoint,Algebraic curve,Algorithm,Triangulation (social science),Software,Witness set,Real algebraic geometry,Cylindrical algebraic decomposition,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
44 | 1 | 0098-3500 |
Citations | PageRank | References |
2 | 0.40 | 23 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel A. Brake | 1 | 17 | 3.56 |
| Daniel J. Bates | 2 | 103 | 12.03 |
| Wenrui Hao | 3 | 4 | 1.48 |
| Jonathan D. Hauenstein | 4 | 269 | 37.65 |
| Andrew J. Sommese | 5 | 412 | 39.68 |
| Charles W. Wampler | 6 | 410 | 44.13 |