On Kolmogorov's Superposition Theorem and its Applications
A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
Autori
Hodnotenie knihy
Viac o knihe
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.
Nákup knihy
On Kolmogorov's Superposition Theorem and its Applications, Jürgen Braun
- Jazyk
- Rok vydania
- 2010
- Väzba
- (mäkká)
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- Titul
- On Kolmogorov's Superposition Theorem and its Applications
- Podtitul
- A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
- Jazyk
- anglicky
- Autori
- Jürgen Braun
- Rok vydania
- 2010
- Väzba
- mäkká
- Počet strán
- 192
- ISBN13
- 9783838116372
- Série
- Hodnotenie
- 3 z 5
- Anotácia
- 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.