On the problems of smoothing and near-interpolation

Kersey, Scott

doi:10.1090/S0025-5718-03-01523-0

On the problems of smoothing and near-interpolation
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Math. Comp. 72 (2003), 1873-1885 Request permission

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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