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The best approximation to C(2) functions and its error bounds using regular-center Gaussian networks
IEEE Transactions on Neural Networks
|January 1, 1994
Summary
Gaussian neural networks can approximate continuous functions. This study provides an upper bound for the approximation error of Gaussian networks, showing error decreases with more neurons.
Area of Science:
- Computational mathematics
- Artificial intelligence
Background:
- Gaussian neural networks are universal approximators.
- Function approximation is crucial in various scientific domains.
Purpose of the Study:
- To establish an upper bound for the approximation error of Gaussian neural networks.
- To analyze the approximation capabilities of Gaussian networks on the unit hypercube.
Main Methods:
- Utilizing the theory of best approximation.
- Analyzing Gaussian networks with centers on a regular mesh in the unit hypercube.
Main Results:
- An upper bound of O(N(-2)) for the approximation error was derived.
- The error bound demonstrates the network's approximation quality.
Conclusions:
- Gaussian neural networks offer a viable method for approximating C(2) functions.
- The derived error bound provides theoretical support for their application in function approximation.
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