Tikhonov Regularization Parameter in Reproducing Kernel Hilbert Spaces with Respect to the Sensitivity of the Solution

Authors:
Kateřina Hlaváčková-Schindler
Affiliations:
Commission for Scientific Visualization, Austrian Academy of Sciences, Vienna, Austria A-1220
Venue:
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Year:
2008

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Abstract

In our paper, we consider Tikhonov regularization in the reproducing Kernel Hilbert Spaces. In this space we derive upper and lower bound of the interval which contains the optimal value of Tikhonov regularization parameter with respect to the sensitivity of the solution without computing the singular values of the corresponding matrix. For the case of normalized kernel, we give an explicit formula for the optimal regularization parameter with respect to the sensitivity of the solution which needs only the knowledge of the minimal singular value of the corresponding matrix.