Name
Title | ||
|---|---|---|
A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity |
Abstract | ||
|---|---|---|
We report on a symbolic-numeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods from knot theory which we combine with computational geometry algorithms in order to compute efficient and accurate results. Nonetheless the problem we are dealing with is ill-posed, in the sense that tiny perturbations in the coefficients of the defining polynomial cause huge errors in the computed results. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1109/SYNASC.2010.41 | SYNASC |
Keywords | Field | DocType |
combinatorial method,defining polynomial,symbolic-numeric algorithm,computational geometry algorithm,accurate result,plane curve singularity,computed result,inexact data,alexander polynomial,knot theory,huge error,computational geometry,accuracy,tin,curve fitting,plane curve,polynomials,convergence,labeling,algebraic curve | Algebra,Polynomial,Bracket polynomial,Algorithm,Reciprocal polynomial,Monic polynomial,Matrix polynomial,Wilkinson's polynomial,Circular algebraic curve,Mathematics,Alexander polynomial | Conference |
ISSN | Citations | PageRank |
2470-8801 | 3 | 0.54 |
References | Authors | |
5 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mădălina Hodorog | 1 | 19 | 3.43 |
| Bernard Mourrain | 2 | 1074 | 113.70 |
| Josef Schicho | 3 | 121 | 21.43 |