Banach Space Valued Neural Network: Ordinary and Fractional Approximation and Interpolation

These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. 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.

Format: Hardback
Length: 423 pages
Publication date: 02 October 2022
Publisher: Springer International Publishing AG

This book delves into the realm of approximation and modernization through the lens of neural network operators. It explores the concept of functions being approximated by neural networks, emphasizing that these functions are valued in Banach spaces. The activation functions employed in these networks derive from a diverse range of sources, including the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. The book showcases various types of approximations, including ordinary, fractional, fuzzy, and stochastic, across univariate, fractional, and multivariate domains. Additionally, it covers iterated-sequential approximations, providing a comprehensive treatment of the subject matter.

The book's findings have the potential to impact numerous fields, including applied mathematics, computer science, and engineering, particularly in the domains of artificial intelligence and machine learning. Furthermore, its applications can extend to applied sciences such as statistics and economics. Consequently, this book serves as a valuable resource for researchers, graduate students, practitioners, and seminar participants across these disciplines, as well as being an essential addition to science and engineering libraries.

The book's exploration of approximation and modernization through neural network operators offers a rich and comprehensive perspective on the field. By examining the diverse range of activation functions and approximations, it provides valuable insights into the potential applications of these techniques in various domains. Whether one is a researcher, graduate student, practitioner, or seminar participant, this book offers valuable knowledge and resources that can enhance one's understanding and expertise in the area.

Weight: 822g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031163999
Edition number: 1st ed. 2023