Название: Contemporary Algorithms: Theory and Applications, Volume I-IV
Автор: Christopher I. Argyros, Samundra Regmi, Ioannis K. Argyros, Santhosh George
Издательство: Nova Science Publishers
Серия: Mathematics Research Developments
Год: 2022-2024
Страниц: 450+424+442+476
Язык: английский
Формат: pdf (true)
Размер: 110.9 MB

This book provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms which are universally applicable are presented in a sound, analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience is required. The organization and content of this book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems.

The Volume II is a continuation of Volume I with the same title. It provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms are presented in a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience are required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems. A new technique is developed to extend the convergence region and provide tighter error estimates of Newton’s Algorithm (NA) for solving generalized equations for Hilbert space- valued operators without additional conditions. The technique is very general, so it can be used to extend the applicability of other algorithms too.

Due to the explosion of technology, scientific and parallel computing, faster computers have become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. There is where this book containing such algorithms comes in handy, with applications in economics, mathematics, biology, chemistry, physics, parallel computing, engineering, and also numerical solution of differential and integral equations. A plethora of problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use algorithms which seem to be the only alternative.