Name
Abstract | ||
|---|---|---|
We describe, for the first time, a completely rigorous homotopy (path-following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial zero are rational our algorithm involves only rational computations, and if the homotopy is well posed an approximate zero with integer coordinates of the target system is obtained. The total bit complexity is linear in the length of the path in the condition metric, and polynomial in the logarithm of the maximum of the condition number along the path, and in the size of the input. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10208-013-9143-2 | Foundations of Computational Mathematics |
Keywords | Field | DocType |
Symbolic–numeric methods,Polynomial systems,Complexity,Condition metric,Homotopy method,Rational computation,Computer proof,14Q20,65H20,68W30 | Condition number,Mathematical optimization,Polynomial,Mathematical analysis,System of polynomial equations,n-connected,UP,Homotopy,Homotopy analysis method,Mathematics,Homotopy lifting property | Journal |
Volume | Issue | ISSN |
13 | 2 | 1615-3375 |
Citations | PageRank | References |
6 | 0.46 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carlos Beltrán | 1 | 102 | 10.04 |
| Anton Leykin | 2 | 173 | 18.99 |