On the problems of smoothing and near-interpolation
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- by Scott N. Kersey PDF
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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.References
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Additional Information
- Scott N. Kersey
- Affiliation: Department of Mathematics, Case Western Reserve University, 10900 Eulcid Avenue, Cleveland, Ohio 44106-7085
- Email: snk@po.cwru.edu
- Received by editor(s): July 20, 1999
- Received by editor(s) in revised form: September 21, 2001
- Published electronically: May 1, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1873-1885
- MSC (2000): Primary 41A05, 41A15, 41A29
- DOI: https://doi.org/10.1090/S0025-5718-03-01523-0
- MathSciNet review: 1986809