The author continues and refines his previous paper “Descartes’ rule of signs for radial basis function neural networks” [Neural Comput. 14, No. 12, 2997‒3011 (2002; Zbl 1079.68597)]. It turns out that radial basis function network is a very useful framework for studying Descartes’ rule of signs. Using this framework the author constructs a counterexample to Grabiner’s conjecture about the number of possible positive and negative zeros of a polynomial and sign changes in a sequence of coefficients of this polynomial.

Reviewer:

Alexander Shapiro (Rishon-le-Zion)