Abstract
A description of spline — or piecewise polynomial functions — involves three characteristics: the nature of their pieces, their location and the smoothness at the connections.
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.
References
J.BERGH–J.PEETRE: On the spaces Vp(o).Boll.Un.Mat. Ital. IV Ser 10 (1974), 632–648
C.de BOOR: On uniform approximation by splines. J.Approx. Theory 1 (1968), 219–262
Ju.A.BRUDNYI: Spline Approximation and functions of bounded variation. Soviet Math.Dokl. Vol,15 (1974), No.2
Ju.A.BRUDNYI: Piecewise polynomial approximation, embedding theorem and rational approximation. Proc.Colloq. Approximation Theory, Bonn 1976, Springer Lecture Notes in Math. No.554
H.G.BURCHARD: On the degree of convergence of piecewise polynomial approximation on optimal meshes. Preprint 1974, to appear
G.BUTLER–F.RICHARDS: An L -saturation theorem for splines. Canad.J.Math. 24 (1972) 957–966
R.DEVORE: Degree of approximation. To appear in Proc.Symp. Approximation Theory, University of Texas, Austin, 1976
R.DEVORE–F.RICHARDS: Saturation and inverse theorems for spline approximation. Spline Functions Approx.Theory, Proc.Symp.Univ.Alberta, Edmonton 1972, ISNM 21 (1973), 73–82
R.DEVORE - K.SCHERER: A constructive theory for approximation by splines with an arbitrary sequence of knot sets. Proc.Co1loq.Approximat ion Theory, Bonn 1976, Springer Lecture Notes in Math. No. 554
H.JOHNEN–K.SCHERER: Direct and inverse theorems for best approximation by A-splines. Proc.Symp. Spline Functions, Karlsruhe 1975, Springer Lecture Notes in Math. 501, pp. 116–131
M.J.MUNTEANU–L.L.SCHUMAKER: Direct and inverse theorems for multi-dimensional spline approximation. Indiana Univ.Math.J. 23 (1973), 461–470
V.A.POPOV: Compt. rend. Acad. bulg. Sci. 26 (1973), 10, 1297
K.SCHERER: Some inverse theorems for best approximation by A-splines. To appear in Proc.Symp.Approximation Theory, University of Texas, Austin 1976
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1977 Springer Science+Business Media New York
About this chapter
Cite this chapter
Scherer, K. (1977). Optimal Degree of Approximation by Splines. In: Micchelli, C.A., Rivlin, T.J. (eds) Optimal Estimation in Approximation Theory. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2388-4_5
Download citation
DOI: https://doi.org/10.1007/978-1-4684-2388-4_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-2390-7
Online ISBN: 978-1-4684-2388-4
eBook Packages: Springer Book Archive