Topology of Critical Points of Computer Functions and Their Detection
by
Khodr Shamseddine
Coauthors: Martin Berz and Kyoko Makino

It is frequently assumed that any critical points that can occur in computer code to be processed by automatic differentiation tools through branching or inherent singularities of intrinsic functions are isolated and distinguishable. Using several examples of various degrees of sophistication, we show that such a naive view is rather misleading; in particular, it is possible to construct computer functions with critical points at nearly every computer number in a certain range. Various methods for the rigorous detection and analysis of these critical points are introduced, including advanced methods based on Levi-Civita numbers, Intervals, and Taylor models.

http://bt.nscl.msu.edu/~hoefkens/ad2000-crt.ps

Date received: March 3, 2000