On Kolmogorov's Superposition Theorem and its Applications

A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions

Autori

• Jürgen Braun

Parametri

• 192 pagine
• 7 ore di lettura

• Natura
• Natura, animali

Maggiori informazioni sul libro

The book introduces a Regularization Network approach utilizing Kolmogorov's superposition theorem to reconstruct higher-dimensional continuous functions from discrete data points. It presents a new constructive proof of the theorem and explores its various versions, linking them to well-known approximation methods and Neural Networks. The work addresses the challenge of the curse of dimensionality, proposing a nonlinear model for function reconstruction within a reproducing kernel Hilbert space. It includes verification and analysis through numerous numerical examples.

Lingua: Inglese

Pubblicato: 2010

(In brossura)