Name
Title | ||
|---|---|---|
A Quadratic Clipping Step with Superquadratic Convergence for Bivariate Polynomial Systems. |
Abstract | ||
|---|---|---|
A new numerical approach to compute all real roots of a system of two bivariate polynomial equations over a given box is described. Using the Bernstein-Bezier representation, we compute the best linear approximant and the best quadratic approximant of the two polynomials with respect to the L-2 norm. Using these approximations and bounds on the approximation errors, we obtain a fat line bounding the zero set first of the first polynomial and a fat conic bounding the zero set of the second polynomial. By intersecting these fat curves, which requires solely the solution of linear and quadratic equations, we derive a reduced subbox enclosing the roots. This algorithm is combined with splitting steps, in order to isolate the roots. It is applied iteratively until a certain accuracy is obtained. Using a suitable preprocessing step, we prove that the convergence rate is 3 for single roots. In addition, experimental results indicate that the convergence rate is superlinear (1.5) for double roots. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s11786-011-0091-4 | Mathematics in Computer Science |
Keywords | Field | DocType |
finding, Polynomial, Bezier clipping | Discrete mathematics,Combinatorics,Hurwitz polynomial,Polynomial,Discriminant,Mathematical analysis,Square-free polynomial,Quadratic function,Root-finding algorithm,Rate of convergence,Matrix polynomial,Mathematics | Journal |
Volume | Issue | ISSN |
5 | 2 | 1661-8270 |
Citations | PageRank | References |
3 | 0.40 | 18 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bert Jüttler | 1 | 1148 | 96.12 |
| Brian Moore | 2 | 3 | 0.40 |