Numerical Infinities and Infinitesimals in Optimization

This book provides a friendly introduction to the Infinity Computer paradigm and its applications in optimization, offering new numerical algorithms, theoretical insights, efficient software implementations, and practical case studies. It was edited by the creator of the Infinity Computer and a leading researcher in optimization, and their results have received scientific prizes. The book opens up new opportunities for researchers, engineers, professors, and students in supercomputing paradigms, optimization, decision-making, game theory, and mathematics and computer science.

Format: Hardback
Length: 365 pages
Publication date: 06 July 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book offers a friendly introduction to the paradigm and presents a wide-ranging overview of the diverse applications of the Infinity Computer in optimization. It delves into groundbreaking numerical algorithms, profound theoretical insights, efficient software implementations, and captivating practical case studies. As the first book to showcase the remarkable advantages of a recently introduced supercomputing paradigm that enables the numerical manipulation of different infinities and infinitesimals on the Infinity Computer, patented in several countries, it stands as a groundbreaking resource for readers interested in optimization.

One of the book's editors is the visionary behind the Infinity Computer, while another editor has been at the forefront of utilizing it in optimization. Their groundbreaking results have earned them numerous prestigious scientific prizes. This engaging book unlocks new horizons for researchers, engineers, professors, and students with a passion for supercomputing paradigms, optimization, decision-making, game theory, and the foundations of mathematics and computer science.

In the realm of mathematics, the handling of infinities has traditionally posed challenges for mathematicians. However, a transformative new approach is emerging, facilitated by the work of Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy. This approach overcomes the traditional discomfort with infinities and opens up a realm of possibilities for mathematical exploration.

The potential impact of these ideas and future hardware prototypes extends across all fields of science that rely on infinite and infinitesimal numbers, such as derivatives, integrals, series, fractals, and more. The introduction of the grossone framework within this paradigm enables computationally efficient handling of infinities, paving the way for groundbreaking advancements in various scientific disciplines.

The editors of this book, along with the contributors, are confident that this new approach will have a profound and lasting impact on mathematics and computer science. The field is poised for significant breakthroughs and innovative developments, thanks to the groundbreaking work presented in this book.

In conclusion, this comprehensive book provides a friendly introduction to the paradigm and presents a wealth of information on the diverse applications of the Infinity Computer in optimization. It serves as a valuable resource for researchers, engineers, scholars, and students alike, as it unlocks new frontiers in supercomputing and mathematical exploration. The future holds great promise for the field, and this book plays a pivotal role in shaping its trajectory.

Weight: 740g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030936419
Edition number: 1st ed. 2022