Abstract
Some methods of nonlinear minimax approximation are discussed. Examples are given to illustrate applicability and numerical behaviour when approximating with splines with free knots, rational functions, sums of exponentials, and functions defined by ordinary differential equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literatur
Ahlberg, J.H., Nilson, E.N., Walsh, J.L.: The Theory of Splines and Their Applications. New York: Academic Press 1967.
Braess, D.: Chebyshev approximation by y-polynomials II. J. Appr. Th. 11, 16–37 (1974).
Cheney, E.W.: Introduction to Approximation Theory. New York: McGraw - Hill 1966.
Cromme, L.: Eine Klasse von Verfahren zur Ermittlung bester nichtlinear Tschebyscheff-Approximationen. erscheint in Numer. Math.
Himmelblau, D.M.: Applied Nonlinear Programming. New York: McGraw - Hill (1972).
Osborne, M.R., Watson, G.A.: An algorithm for minimax-approximation in the nonlinear case. The Computer J. 12, 63–68 (1969).
Reemtsen, R.: Ein Verfahren zur Lösung des diskreten nichtlinearen Tschebyscheff-Problems mit Anwendung auf gewisse nichtlineare Randwertaufgaben bei gewöhnlichen Differentialgleichungen. Diplomarbeit, TH Darmstadt (1975).
Schaback, R.: On Alternation Numbers in Nonlinear Chebyshev Approximation. J. Appr. Th., erscheint demnächst.
Werner, H., Schaback, R.: Praktische Mathematik II, Springer Verlag, Berlin-Heidelberg-New York (1972).
Werner, H.: Vorlesung über Approximationstheorie. Berlin-Heidelberg-New York: Springer, Lecture Notes in Mathematics, vol 14, 1966.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer Basel AG
About this chapter
Cite this chapter
Cromme, L. (1976). Bemerkungen zur Numerischen Behandlung Nichtlinearer Aufgaben der Tschebyscheff-Approximation. In: Collatz, L., Werner, H., Meinardus, G. (eds) Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory. International Series of Numerical Mathematics, vol 30. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7692-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7692-6_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-0824-7
Online ISBN: 978-3-0348-7692-6
eBook Packages: Springer Book Archive