Rational B-splines with prescribed poles (Q1921326)

Given a knot sequence of the compact interval and a pole sequence outside this interval the author defines the rational B-splines by a three term recurrence scheme. When all poles are in infinity the recurrence formula reduces to the one of \textit{C. de Boor} [Splinefunktionen (1990; Zbl 0719.41013)]. The new rational B-splines have some advantages with respect to the similar Chebyshevian B-splines introduced by \textit{T. Lyche} [Constructive Approximation 1, 155-173 (1985; Zbl 0583.41011)].