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| HAL: hal-00359855, version 1 |
| DOI: 10.1007/s00454-007-9042-x |
| Detailed view |  Export this paper |
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| Discrete and Computational Geometry 39, 4 (2008) 639-655 |
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| Certificates of positivity in the bernstein basis |
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| Fatima Boudaoud 1Fabrizio Caruso 2 |
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| (2008) |
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| Let P is an element of Z[X] be a polynomial of degree p with coefficients in the monomial basis of bit-size bounded by tau. If P is positive on [-1, 1], we obtain a certificate of positivity (i.e., a description of P making obvious that it is positive) of bit-size O(p(4)(tau + log(2) p)). Previous comparable results had a bit-size complexity exponential in p and tau (Powers and Reznick in Trans. Am. Math. Soc. 352( 10): 4677 - 4692, 2000; Powers and Reznick in J. Pure Appl. Algebra 164: 221 - 229, 2001). |
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| 1: | Université d'Oran |
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Université d'Oran |
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| 2: | Facolta'' di Scienze Matematiche, Fisiche, e Naturali |
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Università di Pisa |
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| 3: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| hal-00359855, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00359855 | |
| oai:hal.archives-ouvertes.fr:hal-00359855 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Monday, 9 February 2009 15:19:11 | |
| Updated on: Monday, 8 November 2010 11:51:20 | |
