Please use this identifier to cite or link to this item:
https://doi.org/10.1016/j.jco.2008.01.003
DC Field | Value | |
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dc.title | Effective Pólya semi-positivity for non-negative polynomials on the simplex | |
dc.contributor.author | Mok, H.-N. | |
dc.contributor.author | To, W.-K. | |
dc.date.accessioned | 2014-10-28T02:34:13Z | |
dc.date.available | 2014-10-28T02:34:13Z | |
dc.date.issued | 2008-08 | |
dc.identifier.citation | Mok, H.-N., To, W.-K. (2008-08). Effective Pólya semi-positivity for non-negative polynomials on the simplex. Journal of Complexity 24 (4) : 524-544. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jco.2008.01.003 | |
dc.identifier.issn | 0885064X | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/103177 | |
dc.description.abstract | We consider homogeneous polynomials f ∈ R [x1, ..., xn] which are non-negative on the standard simplex in Rn, and we obtain sufficient conditions for such an f to be Pólya semi-positive, that is, all the coefficients of (x1 + ⋯ + xn)N f are non-negative for all sufficiently large positive integers N. Such sufficient conditions are expressed in terms of the vanishing orders of the monomial terms of f along the faces of the simplex. Our result also gives effective estimates on N under such conditions. Moreover, we also show that any Pólya semi-positive polynomial necessarily satisfies a slightly weaker condition. In particular, our results lead to a simple characterization of the Pólya semi-positive polynomials in the low dimensional case when n ≤ 3 as well as the case (in any dimension) when the zero set of the polynomial in the simplex consists of a finite number of points. We also discuss an application to the representations of non-homogeneous polynomials which are non-negative on a general simplex. © 2008 Elsevier Inc. All rights reserved. | |
dc.description.uri | http://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.jco.2008.01.003 | |
dc.source | Scopus | |
dc.subject | Homogeneous polynomials | |
dc.subject | Pólya semi-positivity | |
dc.subject | Simplex | |
dc.subject | Zeros | |
dc.type | Article | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.1016/j.jco.2008.01.003 | |
dc.description.sourcetitle | Journal of Complexity | |
dc.description.volume | 24 | |
dc.description.issue | 4 | |
dc.description.page | 524-544 | |
dc.identifier.isiut | 000258789300004 | |
Appears in Collections: | Staff Publications |
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