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Banach Space Valued Neural Network

Ordinary and Fractional Approximation and Interpolation

  • Book
  • © 2023

Overview

Authors:
  1. George A. Anastassiou

    1. Department of Mathematical Sciences, University of Memphis, Memphis, USA

    View author publications

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  • Presents the generalization and modernization of approximation by neural network operators
  • Provides applications in applied sciences, applied mathematics, and computer science and engineering
  • Is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines

Part of the book series: Studies in Computational Intelligence (SCI, volume 1062)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Algebraic Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations

    • George A. Anastassiou
    Pages 1-41

  3. Gudermannian Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations

    • George A. Anastassiou
    Pages 43-83

  4. Generalized Symmetrical Sigmoid Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations

    • George A. Anastassiou
    Pages 85-108

  5. Abstract Multivariate Algebraic Function Induced Neural Network Approximations

    • George A. Anastassiou
    Pages 109-142

  6. General Multivariate Arctangent Function Induced Neural Network Approximations

    • George A. Anastassiou
    Pages 143-176

  7. Abstract Multivariate Gudermannian Function Induced Neural Network Approximations

    • George A. Anastassiou
    Pages 177-203

  8. Generalized Symmetrical Sigmoid Function Induced Neural Network Multivariate Approximation

    • George A. Anastassiou
    Pages 205-232

  9. Quantitative Approximation by Kantorovich-Choquet Quasi-Interpolation Neural Network Operators Revisited

    • George A. Anastassiou
    Pages 233-253

  10. Quantitative Approximation by Kantorovich-Shilkret Quasi-interpolation Neural Network Operators Revisited

    • George A. Anastassiou
    Pages 255-273

  11. Voronouskaya Univariate and Multivariate Asymptotic Expansions for Sigmoid Functions Induced Quasi-interpolation Neural Network Operators Revisited

    • George A. Anastassiou
    Pages 275-304

  12. Univariate Fuzzy Fractional Various Sigmoid Function Activated Neural Network Approximations Revisited

    • George A. Anastassiou
    Pages 305-349

  13. Multivariate Fuzzy Approximation by Neural Network Operators Induced by Several Sigmoid Functions Revisited

    • George A. Anastassiou
    Pages 351-386

  14. Multivariate Fuzzy-Random and Stochastic Various Activation Functions Activated Neural Network Approximations

    • George A. Anastassiou
    Pages 387-421

  15. Back Matter

    Pages 423-423
    Download chapter PDF
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Keywords

About this book

This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.

Authors and Affiliations

  • Department of Mathematical Sciences, University of Memphis, Memphis, USA

    George A. Anastassiou

Bibliographic Information

  • Book Title: Banach Space Valued Neural Network

  • Book Subtitle: Ordinary and Fractional Approximation and Interpolation

  • Authors: George A. Anastassiou

  • Series Title: Studies in Computational Intelligence

  • DOI: https://doi.org/10.1007/978-3-031-16400-2

  • Publisher: Springer Cham

  • eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-16399-9Published: 02 October 2022

  • Softcover ISBN: 978-3-031-16402-6Published: 03 October 2023

  • eBook ISBN: 978-3-031-16400-2Published: 01 October 2022

  • Series ISSN: 1860-949X

  • Series E-ISSN: 1860-9503

  • Edition Number: 1

  • Number of Pages: XIV, 423

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Computational Intelligence, Artificial Intelligence

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