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 On Kolmogorov's Superposition Theorem and its Applications. A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
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On Kolmogorov's Superposition Theorem and its Applications. A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions

автор Juergen B. издательство Книга по Требованию Математический анализ. Кратные и криволинейные интегралы. Задачи, решения
Cтраниц 192        мягкая обложка       
Аннотация:However, this is not the case, since the involved univariate functions are either unknown or not smooth. Therefore, we develop a Regularization Network approach in a reproducing kernel Hilbert space setting such that the restriction of the underlying approximation spaces defines a nonlinear model for function reconstruction. Additionally, the thesis gives a comprehensive overview on the various versions of KST that exist and its relation to well known approximation schemes and Neural Networks. We present a Regularization Network approach based on Kolmogorov's superposition theorem (KST) to reconstruct higher dimensional continuous functions from their function values on discrete data points. The ansatz is based on a new constructive proof of a version of the theorem. The efficient representation of higher dimensional continuous functions as superposition of univariate continuous functions suggests the conjecture that in a reconstruction, the exponential dependency of the involved numerical costs on the dimensionality, the so-called curse of dimensionality, can be circumvented. Finally, a verification and analysis of the model is given by various numerical examples.
Автор: Juergen B.
Издательство: Книга по Требованию
Год:2010
Цена:
3620 руб
Нет в наличии
Поиск: On Kolmogorov's Superposition Theorem and its Applications. A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
НОВЫЙ ГОД СИМВОЛ 2013 ГОДАУКРАШЕНИЯ
КАРНАВАЛ НА НОВЫЙ ГОД РАСПРОДАЖА
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