A de Casteljau algorithm for generalized Bernstein polynomials

This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case. Dedicated to M. J. D. Powell on the occasion of his 60th birthday