Intelligent systems: approximation by artificial neural networks

This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the 'right' sigmoidaland hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unboundeddomains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases. For the convenience of the reader, the chapters of this book are written in a self-contained style. This treatise relies on author'slast two years of related research work. Advanced courses and seminars can betaught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The exposed results are expected to find applications in many areas of computer science and applied mathematics, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. As such this monograph is suitable for researchers, graduate students, and seminarsof the above subjects, also for all science libraries. First book dealing exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Each chapter is written in a self-contained style, all necessary background and motivations are given per chapter. The exposed results are expected to find applications in many applied areas, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. INDICE: Univariate sigmoidal neural network quantitative approximation. Univariate hyperbolic tangent neural network quantitative approximation. Multivariate sigmoidal neural network quantitative approximation. Multivariate hyperbolic tangent neural network quantitative approximation.

• ISBN: 978-3-642-21430-1
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Cartoné
• Páginas: 108
• Fecha Publicación: 02/06/2011
• Nº Volúmenes: 1
• Idioma: Inglés