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New design for the Descartes rule of signs. (English)
Am. Math. Mon. 111, No. 2, 159-164 (2004).
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)
Classification: I25 A35
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