Recent advances in real complexity and computation / [edited by] Jose Luis Montana and Luis M. Pardo.

Includes bibliographical references.

Topics in real and complex number complexity theory--
Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity--
The complexity and geometry of numerically solving polynomial systems--
On the intrinsic complexity of elimination problems in effective algebraic geometry--
Newton iteration, conditioning and zero counting.

This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ""Recent Advances in Real Complexity and Computation", held July 16-20, 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 Matematica Espanola (RSME).