Name
Title | ||
|---|---|---|
A regularization method for computing approximate invariants of plane curves singularities. |
Abstract | ||
|---|---|---|
We approach the algebraic problem of computing topological invariants for the singularities of a plane complex algebraic curve defined by a squarefree polynomial with inexactly-known coefficients. Consequently, we deal with an ill-posed problem in the sense that, tiny changes in the input data lead to dramatic modifications in the output solution. We present a regularization method for handling the illposedness of the problem. For this purpose, we first design symbolic-numeric algorithms to extract structural information on the plane complex algebraic curve: (i) we compute the link of each singularity by numerical equation solving; (ii) we compute the Alexander polynomial of each link by using algorithms from computational geometry and combinatorial objects from knot theory; (iii) we derive a formula for the delta-invariant and the genus. We then prove the convergence for inexact data of the symbolic-numeric algorithms by using concepts from algebraic geometry and topology. Moreover we perform several numerical experiments, which support the validity for the convergence statement. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1145/2331684.2331692 | Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation |
Keywords | Field | DocType |
plane complex algebraic curve,inexact data,algebraic geometry,input data,alexander polynomial,ill-posed problem,approximate invariants,algebraic problem,computational geometry,convergence statement,plane curves singularity,regularization method,design symbolic-numeric algorithm,algebraic curve,knot theory,genus,regularization,plane curve | Mathematical optimization,Algebraic geometry,Function field of an algebraic variety,Algebra,Algebraic curve,Algebraic cycle,Plane curve,Real algebraic geometry,Delta invariant,Mathematics,Circular algebraic curve | Conference |
Citations | PageRank | References |
3 | 0.42 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mădălina Hodorog | 1 | 19 | 3.43 |
| Josef Schicho | 2 | 3 | 0.42 |