Convergence of an algorithm for constructing snakes

We investigate an algorithm for constructing snakes (extremal polynomials introduced by S. Karlin) suggested by Dzyadyk. It is proved that, in the general case, this algorithm is linearly convergent. In the case where the basis functions of the Chebyshev system belong to the classC², this algorithm is quadratically convergent.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 825–832, July, 1994.