AI Mathematics: Advanced Neural Network Approximation
Published on 15. February 2026
Book
Hardback
XIX, 823 pages
978-3-032-15045-5 (ISBN)
Description
This book presents the new idea of going from the neural networks main tools, the activation functions, to convolution integrals and singular integrals approximations. That is the rare case of employing applied mathematics to treat theoretical ones.
Authors introduce and use also the symmetrized neural network operators able to achieve supersonic speeds of convergence.
Authors use a great variety of activation functions. Thus, in this book all presented is original work by the author given at a very general level to cover a maximum number of different kinds of Neural Networks: giving ordinary, fractional, and stochastic approximations. It is presented here univariate, fractional, and multivariate approximations. Iterated-sequential multi-layer approximations are also studied.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
1 s/w Abbildung
XIX, 823 p. 1 illus.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 51 mm
Weight
1412 gr
ISBN-13
978-3-032-15045-5 (9783032150455)
DOI
10.1007/978-3-032-15046-2
Schweitzer Classification
Other editions
Additional editions
George A. Anastassiou
AI Mathematics: Advanced Neural Network Approximation
E-Book
02/2026
Springer
€266.43
Available for download
Person
George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including "Fractional Differentiation Inequalities" (c) 2009, "Fuzzy Mathematics: Approximation Theory" (c) 2010, "Intelligent Systems: Approximation by Artificial Neural Networks" (c) 2014, "The History of Approximation Theory" (c) 2005, "Modern Differential Geometry in Gauge Theories" (c) 2006, and more.
Razvan Alex Mezei received his PhD from the University of Memphis and currently holds an assistant professorship and Lenoir-Rhyne University, Hickory, North Carolina. He teaches mathematics as well as computer science/IT courses to undergraduates and is a computing sciences program coordinator. Mezei has extensive experience in computer programming and software development and has written several publications with George Anastassiou.
Content
Degree of Approximation by Parametrized logistic activated convolution operators.- Approximation by Parametrized logistic activated Multivariate convolution operators.- Degree of Approximation by symmetrized and perturbed hyperbolic tangent activated convolution operators.- Approximation by Symmetrized and Perturbed Hyperbolic Tangent activated Multivariate convolution operators.- Symmetrized and perturbed hyperbolic tangent neural network multivariate approximation over infinite domains.