Name
Abstract | ||
|---|---|---|
We present a method for solving arbitrary systems of N nonlinear polynomials in n variables over an n-dimensional simplicial domain based on polynomial representation in the barycentric Bernstein basis and subdivision. The roots are approximated to arbitrary precision by iteratively constructing a series of smaller bounding simplices. We use geometric subdivision to isolate multiple roots within a simplex. An algorithm implementing this method in rounded interval arithmetic is described and analyzed. We find that when the total order of polynomials is close to the maximum order of each variable, an iteration of this solver algorithm is asymptotically more efficient than the corresponding step in a similar algorithm which relies on polynomial representation in the tensor product Bernstein basis. We also discuss various implementation issues and identify topics for further study. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s00371-007-0184-x | The Visual Computer |
Keywords | Field | DocType |
solver algorithm,similar algorithm,barycentric bernstein basis,maximum order,engineering design,geometric modeling,arbitrary precision,distance computation,intersections,nonlinear polynomial system,cad,n nonlinear polynomial,bernstein basis,cam,geometric subdivision,cagd,arbitrary system,solid modeling,polynomial representation,interval arithmetic,tensor product,geometric model | Tensor product,Mathematical optimization,Polynomial,Arbitrary-precision arithmetic,Simplex,Bernstein polynomial,Solver,Interval arithmetic,Mathematics,Barycentric coordinate system | Journal |
Volume | Issue | ISSN |
24 | 3 | 1432-2315 |
Citations | PageRank | References |
15 | 0.86 | 10 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Martin Reuter | 1 | 624 | 22.10 |
| Tarjei S. Mikkelsen | 2 | 25 | 2.44 |
| Evan C. Sherbrooke | 3 | 289 | 23.25 |
| Takashi Maekawa | 4 | 449 | 35.38 |
| Nicholas M. Patrikalakis | 5 | 813 | 71.51 |