02772nmm a2200325 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002700139245012000166250001700286260006300303300003300366505028700399653003100686653002800717653003100745653002800776653003200804653001600836041001900852989003600871490004200907028003000949856007200979082001001051520138501061EB000386974EBX0100000000000000024002600000000000000.0cr|||||||||||||||||||||130626 ||| eng a97836422143181 aAnastassiou, George A.00aIntelligent Systems: Approximation by Artificial Neural NetworkshElektronische Ressourcecby George A. Anastassiou a1st ed. 2011 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2011, 2011 aVIII, 108 pbonline resource0 aUnivariate 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 aComputational intelligence aArtificial Intelligence aComputational Intelligence aArtificial intelligence aApplications of Mathematics aMathematics07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aIntelligent Systems Reference Library50a10.1007/978-3-642-21431-840uhttps://doi.org/10.1007/978-3-642-21431-8?nosfx=yxVerlag3Volltext0 a006.3 aThis 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