id: 02074074
dt: j
an: 2007f.00341
au: Schmitt, Michael
ti: New design for the Descartes rule of signs.
so: Am. Math. Mon. 111, No. 2, 159-164 (2004).
py: 2004
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: I25 A35
ut: Descartes rule of signs; radial basis function network; history of
mathematics
ci: Zbl 1079.68597
li: doi:10.2307/4145218
ab: 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.
rv: Alexander Shapiro (Rishon-le-Zion)