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Randomization, Relaxation, and Complexity in Polynomial Equation Solving
Edited by: Leonid Gurvits, Los Alamos National Laboratory, NM, Philippe Pébay, Sandia National Laboratories, Livermore, CA, J. Maurice Rojas, Texas A&M University, College Station, TX, and David Thompson, Sandia National Laboratories, Livermore, CA

Contemporary Mathematics
2011; 217 pp; softcover
Volume: 556
ISBN-10: 0-8218-5228-0
ISBN-13: 978-0-8218-5228-6
List Price: US$79
Member Price: US$63.20
Order Code: CONM/556
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This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28-March 5, 2010 in Banff, Alberta, 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.


Graduate students and research mathematicians interested in algorithms in algebraic geometry.

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