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Conference Paper (international conference)

Tikhonov regularization parameter in reproducing kernel Hilbert Spaces with respect to the sensitivity of the solution

Hlaváčková-Schindler Kateřina

: Artificial Neural Networks - ICANN 2008, p. 215-224 , Eds: Kůrková V., Neruda R., Koutník J.

: International Conference on Neural Networks, Prague, September 2008, (Diplomat Hotel, Prague, CZ, 03.09.2008-06.09.2008)

: CEZ:AV0Z10750506

: 2C06001, GA MŠk

: regularization, reproducing Kernel, Hilbert Spaces

: http://library.utia.cas.cz/separaty/2009/AS/schindler-tikhonov regularization parameter in reproducing kernel hilbert spaces with respect to the sensitivity of the solution.pdf

(eng): 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.

(cze): Uvažujeme Tichonovovu regularizaci v Hilbertových prostorech s reprodukujícími se jádry. Odvozujeme interval obsahující optimální hodnotu Tichonovova regularizačního parametru. Pro normalizované jádro poskytujeme explicitní formuli pro tento parametr. Ta je založena jen na minimální singulární hodnotě odpovídající matice.

: BB

2019-01-07 08:39