Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2759

Full Length Research Paper

BKK-Type bound on the zeros of spline functions

Dian-xuan Gong1, Chuanan Wei2* and Ling Wang1
1College of Sciences, Hebei Polytechnic Universtiy, Tangshan 063009, China. 2Department of Information Technology, Hainan Medical College, Haikou 571101, China.
Email: [email protected]

  •  Accepted: 06 January 2011
  •  Published: 23 January 2012


It was shown by Bernstein that the number of roots in  of a polynomial system depended only on the Newton polytopes of the system for almost all specializations of the coefficients. This result henceforth is referred to as the BKK bound and it gives an upper bound on the number of roots of a polynomial system. But this bound is only applicable to the systems of polynomials. In this paper, the BBK bound was generalized in certain cases of the systems of B-spline function. For the general case, a conjecture was presented.


Key words: The BKK bound, Newton polytope, B-spline, Minkowski mixed volume.