Solving nonlinear polynomial systems in the barycentric Bernstein basis
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Reuter_Solving nonlinear.pdf
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Author(s)
Reuter, Martin
Mikkelsen, Tarjei Sigurd
Sherbrooke, Evan C.
Maekawa, Takashi
Patrikalakis, Nicholas M.
Date Issued
November 2007
Journal
Visual Computer
Publisher
Spring Berlin/Heidelberg
Citation
Reuter, Martin et al. “Solving Nonlinear Polynomial Systems in the Barycentric Bernstein Basis.” The Visual Computer 24.3 (2007) : 187-200. © 2007 Springer-Verlag
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1007/s00371-007-0184-x
