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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2010
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v45_n4_p434_Jeronimo http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo |
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| 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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