Convergence of an algorithm for constructing snakes
- 19 Downloads
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.
KeywordsBasis Function Extremal Polynomial Chebyshev System
Unable to display preview. Download preview PDF.
- 1.L. B. Shevchuk,Construction of Snakes and Their Applications [in Russian], Candidate of Sciences Dissertation (Physics and Mathematics), Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989).Google Scholar
- 2.V. K. Dzyadyk,Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).Google Scholar
- 3.M. G. Krein and A. A. Nudel'man,Markov Moment Problem and Extremal Problems [in Russian], Nauka, Moscow (1976).Google Scholar
- 4.V. F. Dem'yanov and V. N. Malozemov,Introduction to Minimax [in Russian], Nauka, Moscow (1972).Google Scholar
- 5.E. Ya. Remez,Fundamentals of the Numerical Methods of Chebyshev Approximation [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
- 6.V. V. Kovtunets, “A generalization of S. N. Bernstein's parametric method,”Ukr. Mat. Zh.,35, No. 6, 689–695 (1983).Google Scholar
- 7.L. Collatz and W. Krabs,Approximations Theorie. Tschebyscheffsche Approximation mit Anwendungen, Teubner, Stuttgart (1973).Google Scholar