Solving nonlinear polynomial systems in the barycentric Bernstein basis

Martin Reuter*, Tarjei S. Mikkelsen, Evan C. Sherbrooke, Takashi Maekawa, Nicholas M. Patrikalakis

*この研究の対応する著者

研究成果: Article査読

22 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)187-200
ページ数14
ジャーナルVisual Computer
24
3
DOI
出版ステータスPublished - 2008 3
外部発表はい

ASJC Scopus subject areas

  • ソフトウェア
  • コンピュータ ビジョンおよびパターン認識
  • コンピュータ グラフィックスおよびコンピュータ支援設計

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