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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.

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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.

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From the reviews:

"The present work is devoted to the study of convergence rates and upper bounds of approximation errors. ... Throughout all chapters of the book the same method, the same construction is used. ... The book has 107 pages and references are added to each chapter. The formal presentation by the Springer Verlag is excellent." (Claudia Simionescu-Badea, Zentralblatt MATH, Vol. 1243, 2012)

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