Name
Title | ||
|---|---|---|
Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety |
Abstract | ||
|---|---|---|
Systems of polynomial equations arise throughout mathematics, engineering, and the sciences. It is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems. The focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions of polynomial systems: numerical homotopy continuation and symbolic computation. Several illustrative examples are considered, using the software packages Bertini and Singular. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.amc.2013.12.165 | Applied Mathematics and Computation |
Keywords | Field | DocType |
solution set,symbolic computation,illustrative example,numerical homotopy continuation,probabilistic algorithm,fundamental problem,different approach,polynomial equation,application area,polynomial system,affine algebraic variety | Dimension of an algebraic variety,Symbolic-numeric computation,Mathematical optimization,Algebra,Polynomial,Mathematical analysis,System of polynomial equations,Symbolic computation,Algebraic function,Gröbner basis,Polynomial sequence,Mathematics | Journal |
Volume | ISSN | Citations |
231, | 0096-3003 | 2 |
PageRank | References | Authors |
0.38 | 19 | 8 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel J. Bates | 1 | 103 | 12.03 |
| Wolfram Decker | 2 | 26 | 8.41 |
| Jonathan D. Hauenstein | 3 | 269 | 37.65 |
| Chris Peterson | 4 | 68 | 10.93 |
| Gerhard Pfister | 5 | 83 | 12.74 |
| Frank-Olaf Schreyer | 6 | 10 | 3.98 |
| Andrew J. Sommese | 7 | 412 | 39.68 |
| Charles W. Wampler | 8 | 410 | 44.13 |