On the minimum of a positive polynomial over the standard simplex
We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coeffi...
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| Autores principales: | , |
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| Formato: | Artículo publishedVersion |
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2010
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v45_n4_p434_Jeronimo_oai |
| Aporte de: |
| Sumario: | We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex. © 2010 Elsevier Ltd. All rights reserved. |
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