Minimization and Positivity of the Tensorial Rational Bernstein Form

Tareq Hamadneh; Nikolaos Athanasopoulos; Mohammed Ali

doi:10.1109/JEEIT.2019.8717503

Minimization and Positivity of the Tensorial Rational Bernstein Form

Tareq Hamadneh, Nikolaos Athanasopoulos, Mohammed Ali

School of Electronics, Electrical Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

24 Citations (Scopus)

284 Downloads (Pure)

Abstract

Polynomials and rational functions of total degree l defined on n dimensional box have a representation in the Bernstein form. The range of these functions is bounded by the smallest and the largest Bernstein coefficients. In this paper, bounding properties of the range of monomials are extended to the multivariate rational Bernstein case. First, algebraic identities certifying the positivity of a given rational function over a box are addressed. Subsequently, we investigate certificates of positivity by minimization, and bounding functions which are independent of the given dimension.

Original language	English
Title of host publication	2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology 09/04/2019 → 11/04/2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	474-479
ISBN (Electronic)	978-1-5386-7942-5
DOIs	https://doi.org/10.1109/JEEIT.2019.8717503
Publication status	Published - 20 May 2019
Event	2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology - Duration: 09 Apr 2019 → 11 Apr 2019

Conference

Conference	2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology
Period	09/04/2019 → 11/04/2019

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Minimization and Positivity of the Tensorial Rational Bernstein Form
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title = "Minimization and Positivity of the Tensorial Rational Bernstein Form",

abstract = "Polynomials and rational functions of total degree l defined on n dimensional box have a representation in the Bernstein form. The range of these functions is bounded by the smallest and the largest Bernstein coefficients. In this paper, bounding properties of the range of monomials are extended to the multivariate rational Bernstein case. First, algebraic identities certifying the positivity of a given rational function over a box are addressed. Subsequently, we investigate certificates of positivity by minimization, and bounding functions which are independent of the given dimension.",

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Hamadneh, T, Athanasopoulos, N & Ali, M 2019, Minimization and Positivity of the Tensorial Rational Bernstein Form. in 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology 09/04/2019 → 11/04/2019. Institute of Electrical and Electronics Engineers Inc., pp. 474-479, 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology, 09/04/2019. https://doi.org/10.1109/JEEIT.2019.8717503

Minimization and Positivity of the Tensorial Rational Bernstein Form. / Hamadneh, Tareq; Athanasopoulos, Nikolaos; Ali, Mohammed.
2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology 09/04/2019 → 11/04/2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 474-479.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

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AU - Ali, Mohammed

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N2 - Polynomials and rational functions of total degree l defined on n dimensional box have a representation in the Bernstein form. The range of these functions is bounded by the smallest and the largest Bernstein coefficients. In this paper, bounding properties of the range of monomials are extended to the multivariate rational Bernstein case. First, algebraic identities certifying the positivity of a given rational function over a box are addressed. Subsequently, we investigate certificates of positivity by minimization, and bounding functions which are independent of the given dimension.

AB - Polynomials and rational functions of total degree l defined on n dimensional box have a representation in the Bernstein form. The range of these functions is bounded by the smallest and the largest Bernstein coefficients. In this paper, bounding properties of the range of monomials are extended to the multivariate rational Bernstein case. First, algebraic identities certifying the positivity of a given rational function over a box are addressed. Subsequently, we investigate certificates of positivity by minimization, and bounding functions which are independent of the given dimension.

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DO - 10.1109/JEEIT.2019.8717503

M3 - Conference contribution

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BT - 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology 09/04/2019 → 11/04/2019

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Minimization and Positivity of the Tensorial Rational Bernstein Form

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