Name
Abstract | ||
|---|---|---|
In this paper we present methods for the computation ofroots of univariate and bivariate nonlinear polynomial systemsas well as the identification of their multiplicity. Wefirst present an algorithm, called the TDB algorithm, whichcomputes the values and the multiplicities of roots of a univariatepolynomial. The procedure is based on the conceptof the degree of a certain Gauss map, which is deduced fromthe polynomial itself. In the bivariate case, we use a combinationof resultants and our procedure for the univariatecase, as the basis for developing an algorithm for locatingthe roots and computing their multiplicities. Our methodsare robust and global in nature. Complexity analysis ofthe proposed methods is included together with comparisonwith standard subdivision methods. Examples illustrateour techniques. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1109/SMI.2004.45 | SMI |
Keywords | Field | DocType |
topological degree,complexity analysis ofthe,nonlinear polynomial systems,present method,cauchy index,tdb algorithm,combinationof resultant,comparisonwith standard subdivision method,gauss map,multiple roots,bivariate case,certain gauss map,computation ofroots,bivariate nonlinear polynomial,fromthe polynomial,univariate and bi- variate polynomials,indexation,polynomials,nonlinear equations,robustness,computational complexity,control theory,clustering algorithms,floating point arithmetic,gaussian processes,high performance computing,computational geometry | Discrete mathematics,Applied mathematics,Polynomial,Cauchy index,Square-free polynomial,Multiplicity (mathematics),Bivariate analysis,Univariate,Properties of polynomial roots,Mathematics,Computational complexity theory | Conference |
ISBN | Citations | PageRank |
0-7695-2075-8 | 5 | 0.50 |
References | Authors | |
9 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ki Hyoung Ko | 1 | 227 | 20.76 |
| Takis Sakkalis | 2 | 347 | 34.52 |
| Nicholas M. Patrikalakis | 3 | 813 | 71.51 |