Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions

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2017
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Zusammenfassung

Tests for speeding up the determination of the Bernstein enclosure of the range of a multivariate polynomial and a rational function over a box and a simplex are presented. In the polynomial case, this enclosure is the interval spanned by the minimum and the maximum of the Bernstein coefficients which are the coefficients of the polynomial with respect to the tensorial or simplicial Bernstein basis. The methods exploit monotonicity properties of the Bernstein coefficients of monomials as well as a recently developed matrix method for the computation of the Bernstein coefficients of a polynomial over a box.

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Fachgebiet (DDC)
510 Mathematik
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Multivariate polynomial, multivariate rational function, Bernstein coefficient, tensorial Bernstein form, simplicial Bernstein form, range enclosure
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ISO 690TITI, Jihad, Jürgen GARLOFF, 2017. Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions
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@techreport{Titi2017Deter-39178,
  year={2017},
  series={Konstanzer Schriften in Mathematik},
  title={Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions},
  number={361},
  author={Titi, Jihad and Garloff, Jürgen}
}
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