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Mathematics of Computation

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On the problems of smoothing and near-interpolation

Author: Scott N. Kersey
Journal: Math. Comp. 72 (2003), 1873-1885
MSC (2000): Primary 41A05, 41A15, 41A29
Published electronically: May 1, 2003
MathSciNet review: 1986809
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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.

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Additional Information

Scott N. Kersey
Affiliation: Department of Mathematics, Case Western Reserve University, 10900 Eulcid Avenue, Cleveland, Ohio 44106-7085

Keywords: Near-interpolation, smoothing splines, approximation
Received by editor(s): July 20, 1999
Received by editor(s) in revised form: September 21, 2001
Published electronically: May 1, 2003
Article copyright: © Copyright 2003 American Mathematical Society