Intelligent Systems: Approximation by Artificial Neural Networks

George A. Anastassiou

ISBN 10: 3642268552 / ISBN 13: 9783642268557

Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 2013, 2013

Beschreibung

This item is printed on demand - Print on Demand Titel. Neuware -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' sigmoidal and 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 unbounded domains. 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's last two years of related research work. Advanced courses and seminars can be taught 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 seminars of the above subjects, also for all science libraries.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 116 pp. Englisch.

Bestandsnummer des Verkäufers 9783642268557

Bibliografische Details

• Titel: Intelligent Systems: Approximation by Artificial Neural Networks
• Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 2013
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 3642268552
• ISBN-13: 9783642268557
• Einband: Taschenbuch
• Zustand: Neu

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Inhaltsangabe

This brief monograph is the first to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Each chapter is written in a self-contained style, with all necessary background and motivations included.

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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" sigmoidal and 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 unbounded domains. 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's last two years of related research work.
Advanced courses and seminars can be taught 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 seminars of the above subjects, also for all science libraries.