On the problems of smoothing and near-interpolation |
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Authors: | Scott N Kersey |
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Institution: | Department of Mathematics, Case Western Reserve University, 10900 Eulcid Avenue, Cleveland, Ohio 44106-7085 |
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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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Keywords: | Near-interpolation smoothing splines approximation |
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