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Algorithms for Optimal Smoothing Parameter

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
Chapter

Abstract

As before, let the linear continuous operators A : X → Z, T : XY 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 σX in the following way
$$\sigma = \arg \mathop {\min }\limits_{u \in X,{A_u} = z} ||{T_u}||Y$$
(12.1)
and for the smoothing spline σα ∈ X with α > 0
$${\sigma _\alpha } = \arg \mathop {\min \alpha }\limits_{u \in X} ||{T_u}||\mathop Y\limits^2 + ||{A_u} - z||\mathop Z\limits^2$$
(12.2)

Keywords

Taylor Series Newton Method Spectral Radius Variational Theory Smoothing Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
    • 1
  1. 1.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirskRussia

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