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

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Τίτλος: Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions
Συγγραφείς: Titi, Jihad, Garloff, Jürgen
Έτος έκδοσης: 2017
Συλλογή: University of Konstanz: Konstanz Online Publication Server (KOPS)
Θεματικοί όροι: Multivariate polynomial, multivariate rational function, Bernstein coefficient, tensorial Bernstein form, simplicial Bernstein form, range enclosure, ddc:510
Περιγραφή: 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. ; published
Τύπος εγγράφου: report
Περιγραφή αρχείου: application/pdf
Γλώσσα: English
Relation: Konstanzer Schriften in Mathematik; 489670288
Διαθεσιμότητα: http://nbn-resolving.de/urn:nbn:de:bsz:352-0-410198
Rights: https://rightsstatements.org/page/InC/1.0/
Αριθμός Καταχώρησης: edsbas.E1C4EDE5
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  Data: Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions
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  Data: <searchLink fieldCode="AR" term="%22Titi%2C+Jihad%22">Titi, Jihad</searchLink><br /><searchLink fieldCode="AR" term="%22Garloff%2C+Jürgen%22">Garloff, Jürgen</searchLink>
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  Data: 2017
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  Data: University of Konstanz: Konstanz Online Publication Server (KOPS)
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  Data: <searchLink fieldCode="DE" term="%22Multivariate+polynomial%22">Multivariate polynomial</searchLink><br /><searchLink fieldCode="DE" term="%22multivariate+rational+function%22">multivariate rational function</searchLink><br /><searchLink fieldCode="DE" term="%22Bernstein+coefficient%22">Bernstein coefficient</searchLink><br /><searchLink fieldCode="DE" term="%22tensorial+Bernstein+form%22">tensorial Bernstein form</searchLink><br /><searchLink fieldCode="DE" term="%22simplicial+Bernstein+form%22">simplicial Bernstein form</searchLink><br /><searchLink fieldCode="DE" term="%22range+enclosure%22">range enclosure</searchLink><br /><searchLink fieldCode="DE" term="%22ddc%3A510%22">ddc:510</searchLink>
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  Data: 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. ; published
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      – Text: English
    Subjects:
      – SubjectFull: Multivariate polynomial
        Type: general
      – SubjectFull: multivariate rational function
        Type: general
      – SubjectFull: Bernstein coefficient
        Type: general
      – SubjectFull: tensorial Bernstein form
        Type: general
      – SubjectFull: simplicial Bernstein form
        Type: general
      – SubjectFull: range enclosure
        Type: general
      – SubjectFull: ddc:510
        Type: general
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      – TitleFull: Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions
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