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Focusing on the quantitative approximation capabilities of artificial neural networks, this monograph explores the approximation properties of sigmoidal and hyperbolic tangent operators. It analyzes how well these networks approximate the identity-unit operator in both univariate and multivariate scenarios, across bounded and unbounded domains. The study employs inequalities and considers the modulus of continuity of the functions involved, addressing both real and complex cases to provide a comprehensive understanding of approximation rates.
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Intelligent Systems: Approximation by Artificial Neural Networks, George Anastassiou
- Language
- Released
- 2011
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- (Hardcover)
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- Title
- Intelligent Systems: Approximation by Artificial Neural Networks
- Language
- English
- Authors
- George Anastassiou
- Publisher
- Springer, Berlin
- Released
- 2011
- Format
- Hardcover
- Pages
- 108
- ISBN13
- 9783642214301
- Category
- Mathematics
- Description
- Focusing on the quantitative approximation capabilities of artificial neural networks, this monograph explores the approximation properties of sigmoidal and hyperbolic tangent operators. It analyzes how well these networks approximate the identity-unit operator in both univariate and multivariate scenarios, across bounded and unbounded domains. The study employs inequalities and considers the modulus of continuity of the functions involved, addressing both real and complex cases to provide a comprehensive understanding of approximation rates.