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OverviewThis 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. Full Product DetailsAuthor: Leonid Gurvits , Philippe Pebay , J. Maurice Rojas , David ThompsonPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 556 Weight: 0.426kg ISBN: 9780821852286ISBN 10: 0821852280 Pages: 217 Publication Date: 30 December 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsMultivariate ultrametric root counting by M. Avendano and A. Ibrahim A parallel endgame by D. J. Bates, J. D. Hauenstein, and A. J. Sommese Efficient polynomial system solving by numerical methods by C. Beltran and L. M. Pardo Symmetric determinantal representation of formulas and weakly skew circuits by B. Grenet, E. L. Kaltofen, P. Koiran, and N. Portier Mixed volume computation in solving polynomial systems by T.-L. Lee and T.-Y. Li A search for an optimal start system for numerical homotopy continuation by A. Leykin Complex tropical localization, and coamoebas of complex algebraic hypersurfaces by M. Nisse Randomization, sums of squares, near-circuits, and faster real root counting by O. Bastani, C. J. Hillar, D. Popov, and J. M. Rojas Dense fewnomials by K. Rusek, J. Shakalli, and F. Sottile The numerical greatest common divisor of univariate polynomials by Z. ZengReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |