REPRODUCING KERNEL HILBERT SPACES OF FRACTAL INTERPOLATION FUNCTIONS FOR CURVE FITTING PROBLEMS

Dah-Chin Luor ()
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Dah-Chin Luor: Department of Data Science and Analytics, I-Shou University, No. 1, Sec. 1, Syuecheng Road, Dashu District, Kaohsiung City 84001, Taiwan

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-10

Abstract: In this paper, we show that the spaces of some types of fractal interpolation functions are reproducing kernel Hilbert spaces with two different types of inner products. Then we apply these results to curve fitting problems. We establish the fractal interpolation functions that are in reproducing kernel Hilbert spaces and that minimize the regularized empirical error.

Keywords: Fractal; Interpolation; Fractal Interpolation Function; Curve Fitting; Reproducing Kernel Hilbert Space; Fractal-Type Kernel (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500372

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