On the Problems of Smoothing and Near-Interpolation
Document Type
Article
Publication Date
10-2003
Publication Title
Mathematics of Computation
ISSN
1088-6842
Abstract
In the first part of this paper we apply a saddle point theorem from convex analysis to show that various constrained minimization problems are equivalent to the problem of smoothing by spline functions. In particular, we show that near-interpolants are smoothing splines with weights that arise as Lagrange multipliers corresponding to the constraints in the problem of near-interpolation. In the second part of this paper we apply certain fixed point iterations to compute these weights. A similar iteration is applied to the computation of the smoothing parameter in the problem of smoothing.
Recommended Citation
Kersey, Scott N..
2003.
"On the Problems of Smoothing and Near-Interpolation."
Mathematics of Computation, 72 (244): 1873-1885.
source: https://www.ams.org/journals/mcom/2003-72-244/S0025-5718-03-01523-0/S0025-5718-03-01523-0.pdf
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/536
