Summary
We determine the connected components of the set of normal elements of the family ℛ n m [a,b] of rational functions. Numerical difficulties occuring with the computation of the Chebyshev approximation via the Remez algorithm can be caused by its disconnectedness. In order to illustrate this we give numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Braess, D.: Zur numerischen Stabilität des Newton-Verfahrens bei der nichtlinearen Tschebyscheff-Approximation. Approximation Theory, Proceedings of an International Colloquium Held at Bonn, Germany, June 8–11, 1976, Springer Lecture Notes in Mathematics556, 54–62
Cody, W.J.: A survey of practical rational and polynomial approximation of functions. SIAM Rev.12, 400–423 (1970)
Cody, W.J., Stoer, J.: Rational Chebyshev approximation using interpolation. Numer. Math.9, 177–188 (1966)
Meinardus, G.: Approximation von Funktionen und ihre numerische Behandlung. Berlin: Springer 1964
Werner, H.: Die konstruktive Ermittlung der Tschebyscheff-Approximierenden im Bereich der Rationalen Funktionen. Arch. Rational Mech. Anal.11, 368–384 (1962)
Werner, H.: Starting procedures for the iterative calculation of rational Chebyshev approximation. Proc. IFIP Congress Edinburgh pp. 106–110, 1968
Wetterling, W.: Ein Interpolationsverfahren zur Lösung der linearen Gleichungssysteme, die bei der rationalen Tschebyscheff-Approximation auftreten. Arch. Rational Mech. Anal.12, 403–408 (1963)
Author information
Authors and Affiliations
Additional information
Gefördert von der DFG unter Nr. Be 808/2
Rights and permissions
About this article
Cite this article
Bartke, K. Die Struktur der normalen rationalen Funktionen. Numer. Math. 43, 379–388 (1984). https://doi.org/10.1007/BF01390180
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01390180