Abstract
For givenk-convex data, ak-convex interpolant is sought, so that a certain convex functional related with thek-th derivative is minimized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C.K. Chui, F. Deutsch and J. Ward, Constrained best approximation in Hilbert space, C.A.T. Report no. 151, 1987.
C. de Boor, On ‘best’ interpolation. J. Approx. Theory. 16 (1976) 28–42.
G. Iliev and W. Pollul, Convex interpolation with minimalL ∞-norm of the second derivative, Math. Zeit. 186 (1984) 49–56.
G. Iliev and W. Pollul, Convex interpolation with minimalL p-norm (1<p<∞) of thek-th derivative,Proc. 13th Spring Conf. of the Union of Bulgarian Math., 1984.
L.D. Irvine, S.P. Marin and P.W. Smith, Constrained interpolation and smoothing, Constructive Approximation 2 (1986) 129–151.
C.A. Micchelli, P.W. Smith, J. Swetits and J. Ward, ConstrainedL p approximation, Constructive Approximation 1 (1985) 93–102.
C.A. Micchelli and F. Utreras, Smoothing and interpolation in a convex subset of a Hilbert space, SIAM J. Sci. Stat. Comput. 9 (1988) 728–746.
F.I. Utreras, Positive thin plate splines, Approx. Theory and its Applications 1 (1985) 77–108.
F.I. Utreras and L. Varas, Monotone interpolation of scattered data in ℝ2, Preprint Universidad de Chile.
Author information
Authors and Affiliations
Additional information
Communicated by M. Gasca
Partially supported by C.I.C.Y.T. PS87/0060.
Rights and permissions
About this article
Cite this article
Carnicer, J.M. On best constrained interpolation. Numer Algor 1, 155–176 (1991). https://doi.org/10.1007/BF02142319
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02142319