Contemporary Mathematics 2013; 185 pp; softcover Volume: 604 ISBN10: 0821891502 ISBN13: 9780821891506 List Price: US$76 Member Price: US$60.80 Order Code: CONM/604
 This volume is composed of six contributions derived from the lectures given during the UIMPRSME Lluís Santaló Summer School on "Recent Advances in Real Complexity and Computation", held July 1620, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: "Can a zero of \(n\) complex polynomial equations in \(n\) unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?" These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving. This book is published in cooperation with Real Sociedad Matemática Española (RSME). Readership Graduate students and research mathematicians interested in the complexity of computation. Table of Contents  M. Baartse and K. Meer  Topics in real and complex number complexity theory
 B. Bank, M. Giusti, and J. Heintz  Polar, bipolar and copolar varieties: Real solving and algebraic varieties with intrinsic complexity
 C. Beltrán and M. Shub  The complexity and geometry of numerically solving polynomial systems
 M. Giusti and J.C. Yakoubsohn  Multiplicity hunting and approximating multiple roots of polynomials systems
 J. Heintz, B. Kuijpers, and A. R. Paredes  On the intrinsic complexity of elimination problems in effective algebraic geometry
 G. Malajovich  Newton iteration, conditioning and zero counting
