This volume, LNCS 11973, consists of 34 full and 18 short papers chosen among papers presented at special streams and sessions of the Conference. The papers in part I were organized following the topics of these special sessions: approximation: methods, algorithms, and applications; computational methods for data analysis; first order methods in optimization: theory and applications; high performance computing in modelling and simulation; numbers, algorithms, and applications; optimization and management of water supply.

This volume, LNCS 11974, consists of 19 full and 32 short papers chosen among regular papers presented at the the Conference including also the paper of the winner (Lorenzo Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for the best NUMTA 2019 presentation made by a young scientist.

The papers in part II explore the advanced research developments in such interconnected fields as local and global optimization, machine learning, approximation, and differential equations. A special focus is given to advanced ideas related to methods and applications using emerging computational paradigms.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas:

Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computerscience.

MIT Technology Review

“These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing.

“I am sure that the new approach … will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science.

“Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing.

The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14–20, 2023.The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions.The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.

The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14-20, 2023.

The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions.

The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.

The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14-20, 2023.

The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions.

The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.

This volume, LNCS 11973, consists of 34 full and 18 short papers chosen among papers presented at special streams and sessions of the Conference. The papers in part I were organized following the topics of these special sessions: approximation: methods, algorithms, and applications; computational methods for data analysis; first order methods in optimization: theory and applications; high performance computing in modelling and simulation; numbers, algorithms, and applications; optimization and management of water supply.

This volume, LNCS 11974, consists of 19 full and 32 short papers chosen among regular papers presented at the the Conference including also the paper of the winner (Lorenzo Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for the best NUMTA 2019 presentation made by a young scientist.

The papers in part II explore the advanced research developments in such interconnected fields as local and global optimization, machine learning, approximation, and differential equations. A special focus is given to advanced ideas related to methods and applications using emerging computational paradigms.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas:

Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computerscience.

MIT Technology Review

“These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing.

“I am sure that the new approach … will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science.

“Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing.

The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14–20, 2023.The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions.The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.

The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14-20, 2023.

The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions.

The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.

The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14-20, 2023.

The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions.

The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.