On the roots of certain polynomials arising from the analysis of the Nelder–Mead simplex method Original Research Article

The study of the effect of dimensionality on the Nelder–Mead simplex method for unconstrained optimization leads us to the study of a two parameter family of polynomials of the form pn(z)=b−az−cdots, three dots, centered−azn−1+zn. We show that provided that image is real, it is possible to use, primarily, the Schur–Cohn Criterion in order to determine the configuration of the roots of pn(z) with respect to the unit circle.