Abstract
In this paper the problem of approximating on special subspaces of ℝ2 a given continous real function f in the uniform norm by spline functions with fixed knots is considered. The spline functions are tensor products of B-splines. Using alternation lattices one gets sufficient conditions for the existence and uniquenness of a minimal solution. On halfdiscrete subspaces of ℝ2 also necessary conditions are given.
Keywords
- Spline Function
- Special Subspace
- Dann Gilt
- P61ya Frequency
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Literatur
Barrar, R.B., Loeb, H.L.: Spline Functions with Free Knots as the Limits of Varisolvent Families. J. Approximation Theory 12(1974), 70–77.
Buck, R.C.: Alternation Theorems for Functions of Several Variables. J. Approximation Theory 1(1968), 325–334.
Cheney, E.W.: Introduction to Approximation Theory. Mc Graw-Hill New York 1966.
Curry, H.B., Schoenberg, I.J.: On Pólya Frequency Functions and Their Limits. J. d'Anal. Math 18, 71–107.
Ehlich, H., Haußmann, W.: Tschebyscheff-Approximation stetiger Funktionen in zwei Veränderlichen. Math. Z. 117(1970), 21–34.
Ehlich, H., Zeller, K.: Cebysev-Polynome in mehreren Veränderlichen. Math. Z. 93(1966), 142–143.
Greville, T.N.E.: Introduction to Spline Functions in: Theory and Applications of Spline Functions. Academic Press New York 1969.
Hau\mann, W.: Alternanten bei mehrdimensionaler Tschebyscheff-Approximation. ZAMM 52(1972), T206–T208.
Karlin, S.: Total Positivity, Volume I. Stanford University Press, Stanford California 1968.
Karlin, S., Studden, W.J.: Tschebyscheff Systems: With Applications in Analysis and Statistics. Interscience Publishers New York 1966.
Meinardus, G.: Approximation of Functions: Theory and Numerical Methods. Springer-Verlag Berlin Heidelberg New York 1967.
Rice, J.R.: The Approximation of Functions, Volume II. Addison-Wesley Publishing Company, Reading Massachusetts 1969.
Schumaker, L.: Uniform Approximation by Tschebyscheffian Spline Functions. Journal of Mathematics and Mechanics 18(1968), 369–377.
Schumaker, L.: Approximation by Splines in: Greville, T.N.E.: Theory and Applications of Spline Functions. Academic Press New York 1969.
Sommer, M.: Gleichmäßige Approximation mit zweidimensionalen Splinefunktionen, Dissertation, Universität Erlangen-Nürnberg, 1975.
Strauß, H.: Eindeutigkeit bei der gleichmäßigen Approximation mit Tschebyscheffschen Splinefunktionen. Erscheint in J. Approximation Theory.
Strauß, H.: L1-Approximation mit Splinefunktionen. ISNM 26 Birkhäuser Verlag, Basel und Stuttgart, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
Sommer, M. (1976). Alternanten Bei Gelchmässiger Approximation Mit Zweidimensionalen Splinefunktionen. In: Böhmer, K., Meinardus, G., Schempp, W. (eds) Spline Functions. Lecture Notes in Mathematics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079755
Download citation
DOI: https://doi.org/10.1007/BFb0079755
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07543-1
Online ISBN: 978-3-540-38073-3
eBook Packages: Springer Book Archive
