Titre : | Randomization, relaxation, and complexity in polynomial equation solving : Banff International Research Station Workshop on Randomization, Relaxation, and Complexity February 28–March 5, 2010 Banff, Ontario, Canada | Type de document : | texte imprimé | Auteurs : | Leonid GURVITS, Editeur scientifique ; Philippe PÉBAY, Editeur scientifique ; J. Maurice ROJAS, Editeur scientifique | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | Année de publication : | cop. 2011 | Collection : | Contemporary mathematics, ISSN 0271-4132 num. 556 | Importance : | VIII-217 p. | ISBN/ISSN/EAN : | 978-0-8218-5228-6 | Langues : | Anglais (eng) | Catégories : | 11Y16 12Y05 14M25 14P25 14Q20
| Mots-clés : | théorie des nombres algorithme géométrie algébrique | Résumé : | This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28–March 5, 2010 in Banff, Ontario, Canada. This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale’s 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed. | Note de contenu : | références |
Randomization, relaxation, and complexity in polynomial equation solving : Banff International Research Station Workshop on Randomization, Relaxation, and Complexity February 28–March 5, 2010 Banff, Ontario, Canada [texte imprimé] / Leonid GURVITS, Editeur scientifique ; Philippe PÉBAY, Editeur scientifique ; J. Maurice ROJAS, Editeur scientifique . - American Mathematical Society, cop. 2011 . - VIII-217 p.. - ( Contemporary mathematics, ISSN 0271-4132; 556) . ISBN : 978-0-8218-5228-6 Langues : Anglais ( eng) Catégories : | 11Y16 12Y05 14M25 14P25 14Q20
| Mots-clés : | théorie des nombres algorithme géométrie algébrique | Résumé : | This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28–March 5, 2010 in Banff, Ontario, Canada. This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale’s 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed. | Note de contenu : | références |
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