Gregorio Malajovich (Universidade Federal do Rio de Janeiro)
Calvin Lab 116
Introduction to Alpha-theory
Alpha-theory provides a rigorous way to certify approximate solutions for analytic equations. It was introduced by Steve Smale in the 80's, and is one of the main tools to produce robust path-following algorithms with rigorous complexity estimates.
In this first talk, I will introduce the main invariants and prove the "gamma theorem." The proof of the "alpha theorem" with optimal constant will be given in a subsequent lecture.
This is also the organizational meeting for this seminar.