Reproducing Kernel Hilbert Spaces and fractal interpolation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Bouboulis, P.¹  Mavroforakis, M.² 

[1] Univ Athens, Dept Informat & Telecommun, Athens 15784, Greece

[2] Univ Houston, Dept Comp Sci, Computat Biomed Lab, Houston, TX 77204 USA

关键词: Fractal interpolation;    Reproducing Kernel Hilbert Space;    Kernels;   

DOI  :  10.1016/j.cam.2011.02.003

来源: Elsevier

【 摘 要 】

Reproducing Kernel Hilbert Spaces (RKHSs) are a very useful and powerful tool of functional analysis with application in many diverse paradigms, such as multivariate statistics and machine learning. Fractal interpolation, on the other hand, is a relatively recent technique that generalizes traditional interpolation through the introduction of self-similarity. In this work we show that the functional space of any family of (recurrent) fractal interpolation functions ((R)FIFs) constitutes an RKHS with a specific associated kernel function, thus, extending considerably the toolbox of known kernel functions and introducing fractals to the RKHS world. We also provide the means for the computation of the kernel function that corresponds to any specific fractal RKHS and give several examples. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free