Zeroing Dynamics, Gradient Dynamics, and Newton Iterations

Neural networks and neural dynamics are powerful approaches for solving mathematical problems in science, engineering, and business. Zeroing Dynamics is the first book to show how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. It brings together research in neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.

Format: Paperback / softback
Length: 310 pages
Publication date: 01 January 2021
Publisher: Taylor & Francis Ltd

Neural networks and neural dynamics offer remarkable solutions to complex mathematical problems across diverse fields of science, engineering, and business. In contrast to traditional gradient neural networks limited to static problems with constant coefficient matrices and vectors, the authors present a groundbreaking method called zeroing dynamics, which adeptly tackles time-varying challenges. This innovative approach combines research from neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.

In their comprehensive book titled "Zeroing Dynamics, Gradient Dynamics, and Newton Iterations," the authors delve into the intricate details of accurately and efficiently solving time-varying problems in real-time or online. This groundbreaking work unites various disciplines, providing a comprehensive treatment of both static and dynamic neural networks. Readers will be captivated as they explore how novel theoretical results have been successfully applied to a wide range of practical problems.

The authors meticulously develop, analyze, model, simulate, and compare zeroing dynamics models, enabling the online solution of numerous time-varying problems. These problems encompass diverse domains, including root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving. By leveraging the power of zeroing dynamics, researchers and practitioners can effectively address complex challenges and unlock new opportunities in their respective fields.

This groundbreaking book serves as a valuable resource for researchers, students, and professionals seeking to advance their understanding of neural networks and neural dynamics. It provides a comprehensive foundation for those interested in exploring the latest developments in this field and applying them to real-world problems. With its clear and concise writing style, extensive illustrations, and practical examples, "Zeroing Dynamics, Gradient Dynamics, and Newton Iterations" makes complex concepts accessible to a wide audience.

In conclusion, neural networks and neural dynamics, facilitated by the groundbreaking zeroing dynamics method, represent powerful approaches for solving complex mathematical problems in diverse scientific, engineering, and business domains. The authors' comprehensive book, "Zeroing Dynamics, Gradient Dynamics, and Newton Iterations," offers a valuable guide for researchers and practitioners seeking to leverage the power of these techniques to address real-world challenges and drive innovation. As the field continues to evolve, this book will undoubtedly remain a staple in the literature of neural networks and neural dynamics.

Dimension: 254 x 178 (mm)
ISBN-13: 9781138894082