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.
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Hlaváčková-Schindler, K. (2008). Tikhonov Regularization Parameter in Reproducing Kernel Hilbert Spaces with Respect to the Sensitivity of the Solution. In: Kůrková, V., Neruda, R., Koutník, J. (eds) Artificial Neural Networks - ICANN 2008. ICANN 2008. Lecture Notes in Computer Science, vol 5163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87536-9_23
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DOI: https://doi.org/10.1007/978-3-540-87536-9_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87535-2
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