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Detecting positivity of multi- variable polynomials on the standard simplex using the the Bernstein-Bezi

Velde, R. te (2011) Detecting positivity of multi- variable polynomials on the standard simplex using the the Bernstein-Bezi. Master's Thesis / Essay, Mathematics.

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Abstract

One can read about algorithmic copositivity detection by simplicial partition in a paper of Stefan Bundfuss and Mirjam Dür. Copositivity detection is a quadratic problem (for quadratic polynomials). In this paper we did a similar approach, but for general multi-index polynomials instead of quadratic polynomials. Herefore, we use multi-index notations, barycentric coordinates, the Bernstein-Bezi´er representation of polynomials and simplicial partition. In this thesis, one can read about al the theory behind Bernstein-Bezi´er with respect to the positivity of polynomials on the standard simplex. Furthermore, we made several algorithms for low degree polynomials with one and two variables. We concluded that the algorithm works well except for some cases that the local minimum of a polynomial is exactly zero. The last conclusion is that the use of the Bernstein-Bezi´er form for positivity evaluations certainly has potential, but describing a complex polynomial with Bernstein-coefficients is rather hard and complicated.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:55
Last Modified: 15 Feb 2018 07:55
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/11339

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