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Kolmogorov Superpositions: A New Computational Algorithm

Kolmogorov Superpositions: A New Computational Algorithm
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Author(s): David Sprecher (University of California at Santa Barbara, USA)
Copyright: 2013
Pages: 27
Source title: Efficiency and Scalability Methods for Computational Intellect
Source Author(s)/Editor(s): Boris Igelnik (BMI Research, Inc., USA)and Jacek M. Zurada (University of Louisville, USA)
DOI: 10.4018/978-1-4666-3942-3.ch011

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Abstract

Kolmogorov’s superpositions enable the representation of every real-valued continuous function f defined on the Euclidean n-cube in the form , with continuous functions that compute f, and fixed continuous functions dependent only on n. The functions specify space-filling curves that determine characteristics that are not suitable for efficient computational algorithms. Reversing the process, we specify suitable space-filling curves that enable new functions that give a computational algorithm better adaptable to applications. Detailed numerical constructions are worked out for the case n = 2.

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