On the Problems of Smoothing and Near-Interpolation

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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.

Original languageAmerican English
JournalMathematics of Computation
Volume72
StatePublished - Oct 1 2003

Keywords

  • Near-Interpolation
  • Smoothing

DC Disciplines

  • Education
  • Mathematics

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