Algorithms for Optimal Smoothing Parameter

Anatoly Yu. Bezhaev and Vladimir A. Vasilenko
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Vladimir A. Vasilenko: Institute of Computational Mathematics and Mathematical Geophysics

Chapter Chapter 12 in Variational Theory of Splines, 2001, pp 243-262 from Springer

Abstract: Abstract As before, let the linear continuous operators A : X → Z, T : X → Y be defined in the Hilbert spaces, z be an element of the space Z. Present as in Chapter 1 the variational principle for the interpolating spline σ ∈ X in the following way (12.1) $$\sigma = \arg \mathop {\min }\limits_{u \in X,{A_u} = z} ||{T_u}||Y$$ and for the smoothing spline σα ∈ X with α > 0 (12.2) $${\sigma _\alpha } = \arg \mathop {\min \alpha }\limits_{u \in X} ||{T_u}||\mathop Y\limits^2 + ||{A_u} - z||\mathop Z\limits^2$$

Keywords: Taylor Series; Newton Method; Spectral Radius; Variational Theory; Smoothing Parameter (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4757-3428-7_12

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