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Cited by 75

A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities

A Dynamic Precision Floating-Point Arithmetic Based on the Infinity Computer Framework

Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro, Francesca Mazzia

https://doi.org/10.1007/978-3-030-40616-5_22

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11974 (2020), p. 289

A Grossone-Based Numerical Model for Computations with Infinity: A Case Study in an Italian High School

Francesco Ingarozza, Maria Teresa Adamo, Maria Martino, Aldo Piscitelli

https://doi.org/10.1007/978-3-030-39081-5_39

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 451

A New Computational Approach to Infinity for Modelling Physical Phenomena

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-00297-2_35

Book Springer Proceedings in Physics (Frontiers of Fundamental Physics and Physics Education Research) Volume 145 (2014), p. 353

A New Computational Methodology Using Infinite and Infinitesimal Numbers

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-642-15979-4_72

Book Lecture Notes in Computer Science (Cellular Automata) Volume 6350 (2010), p. 646

A New Syntax for Diagrammatic Logic: A Generic Figures Approach

Gianluca Caterina, Rocco Gangle

https://doi.org/10.1007/978-3-030-40616-5_4

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11974 (2020), p. 43

A classification of one-dimensional cellular automata using infinite computations

Louis D’Alotto

https://doi.org/10.1016/j.amc.2014.06.087

Journal Applied Mathematics and Computation Volume 255 (2015), p. 15

A dual number formulation to efficiently compute higher order directional derivatives

R. Peón-Escalante, K.B. Cantún-Avila, O. Carvente, A. Espinosa-Romero, F. Peñuñuri

https://doi.org/10.1016/j.jocs.2024.102217

Journal Journal of Computational Science Volume 76 (2024), p. 102217

A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic

P. Amodio, F. Iavernaro, F. Mazzia, M.S. Mukhametzhanov, Ya.D. Sergeyev

https://doi.org/10.1016/j.matcom.2016.03.007

Journal Mathematics and Computers in Simulation Volume 141 (2017), p. 24

A method of formalizing computer operations for solving nonlinear differential equations

Vladimir Aristov, Andrey Stroganov

https://doi.org/10.1016/j.amc.2011.09.029

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8083

A new approach to the Z-transform through infinite computation

Fabio Caldarola, Mario Maiolo, Viviana Solferino

https://doi.org/10.1016/j.cnsns.2019.105019

Journal Communications in Nonlinear Science and Numerical Simulation Volume 82 (2020), p. 105019

AIP Conference Proceedings

Claudia Roberta Calidonna, Salvatore Di Gregorio, Francesco Gullace, Daniel Gullì, Valeria Lupiano

https://doi.org/10.1063/1.4952339

Conference Volume 1738 (2016), p. 480103

AIP Conference Proceedings

Yaroslav D. Sergeyev

https://doi.org/10.1063/1.5043649

Conference Volume 1978 (2018), p. 020004

AIP Conference Proceedings

Yaroslav D. Sergeyev

https://doi.org/10.1063/1.4951756

Conference Volume 1738 (2016), p. 020012

AIP Conference Proceedings

Louis D’Alotto

https://doi.org/10.1063/1.4965309

Conference Volume 1776 (2016), p. 020003

AIP Conference Proceedings

F. Mazzia, Ya. D. Sergeyev, F. Iavernaro, P. Amodio, M. S. Mukhametzhanov

https://doi.org/10.1063/1.4965397

Conference Volume 1776 (2016), p. 090033

AIP Conference Proceedings

Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev

https://doi.org/10.1063/1.4965404

Conference Volume 1776 (2016), p. 090040

Addressing Ill-Conditioning in Global Optimization Using a Software Implementation of the Infinity Computer

Marat S. Mukhametzhanov, Dmitri E. Kvasov

https://doi.org/10.1007/978-3-030-93642-6_14

Book Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 347

An application of Grossone to the study of a family of tilings of the hyperbolic plane

Maurice Margenstern

https://doi.org/10.1016/j.amc.2011.04.014

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8005

Applications of finite and infinite Fourier series in heat processes with impulse data

S. Faydaoglu, V.G. Yakhno

https://doi.org/10.1016/j.amc.2011.08.093

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8120

Cellular automata using infinite computations

Louis D’Alotto

https://doi.org/10.1016/j.amc.2011.10.065

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8077

Combinators as Observable Presheaves: A Characterization in the Grossone Framework

Rocco Gangle, Fernando Tohmé, Gianluca Caterina

https://doi.org/10.1007/978-3-031-81247-7_7

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 14478 (2025), p. 84

Computations with Grossone-Based Infinities

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-21819-9_6

Book Lecture Notes in Computer Science (Unconventional Computation and Natural Computation) Volume 9252 (2015), p. 89

Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs

Fernando Tohmé, Gianluca Caterina, Rocco Gangle

https://doi.org/10.1016/j.amc.2020.125343

Journal Applied Mathematics and Computation Volume 385 (2020), p. 125343

Computing sums of conditionally convergent and divergent series using the concept of grossone

Anatoly Zhigljavsky

https://doi.org/10.1016/j.amc.2011.12.034

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8064

Conjugate-symplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer

F. Iavernaro, F. Mazzia, M.S. Mukhametzhanov, Ya.D. Sergeyev

https://doi.org/10.1016/j.apnum.2019.06.011

Journal Applied Numerical Mathematics Volume 155 (2020), p. 58

Counting systems and the First Hilbert problem

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.na.2009.09.009

Journal Nonlinear Analysis: Theory, Methods & Applications Volume 72, Issue 3-4 (2010), p. 1701

Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.chaos.2009.04.013

Journal Chaos, Solitons & Fractals Volume 42, Issue 5 (2009), p. 3042

Examples of the Usage of Infinities and Infinitesimals in Numerical Computations

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-12745-3_15

Book Communications in Computer and Information Science (Advances in Artificial Life and Evolutionary Computation) Volume 445 (2014), p. 190

Fibonacci words, hyperbolic tilings and grossone

Maurice Margenstern

https://doi.org/10.1016/j.cnsns.2014.07.032

Journal Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 3

Finite and Infinite Computations and a Classification of Two-Dimensional Cellular Automata Using Infinite Computations

Louis D’Alotto

https://doi.org/10.1007/978-3-319-62932-2_17

Book Lecture Notes in Computer Science (Parallel Computing Technologies) Volume 10421 (2017), p. 183

Grossone Methodology for Lexicographic Mixed-Integer Linear Programming Problems

Marco Cococcioni, Alessandro Cudazzo, Massimo Pappalardo, Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-030-40616-5_28

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11974 (2020), p. 337

Higher order numerical differentiation on the Infinity Computer

Yaroslav D. Sergeyev

https://doi.org/10.1007/s11590-010-0221-y

Journal Optimization Letters Volume 5, Issue 4 (2011), p. 575

Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite

Yaroslav D. Sergeyev

https://doi.org/10.1007/s10699-018-9566-y

Journal Foundations of Science Volume 24, Issue 1 (2019), p. 153

Infinigons of the hyperbolic plane and grossone

Maurice Margenstern

https://doi.org/10.1016/j.amc.2016.01.019

Journal Applied Mathematics and Computation Volume 278 (2016), p. 45

Infinite Games on Finite Graphs Using Grossone

Louis D’Alotto

https://doi.org/10.1007/978-3-030-40616-5_29

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11974 (2020), p. 346

Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves

Luigi Antoniotti, Fabio Caldarola, Mario Maiolo

https://doi.org/10.1007/s00009-020-01531-5

Journal Mediterranean Journal of Mathematics Volume 17, Issue 3 (2020)

Infinite computations and the generic finite

Louis H. Kauffman

https://doi.org/10.1016/j.amc.2014.06.054

Journal Applied Mathematics and Computation Volume 255 (2015), p. 25

Infinite games on finite graphs using grossone

Louis D’Alotto

https://doi.org/10.1007/s00500-020-05167-1

Journal Soft Computing Volume 24, Issue 23 (2020), p. 17509

Infinitesimal Probabilities Based on Grossone

Cristian S. Calude, Monica Dumitrescu

https://doi.org/10.1007/s42979-019-0042-8

Journal SN Computer Science Volume 1, Issue 1 (2020)

Infinitesimals and infinites in the history of mathematics: A brief survey

Gabriele Lolli

https://doi.org/10.1016/j.amc.2011.08.092

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 7979

Infinity computations in cellular automaton forest-fire model

D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa

https://doi.org/10.1016/j.cnsns.2014.06.031

Journal Communications in Nonlinear Science and Numerical Simulation Volume 20, Issue 3 (2015), p. 861

Interpretation of percolation in terms of infinity computations

D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa

https://doi.org/10.1016/j.amc.2011.11.044

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8099

Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm

Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev

https://doi.org/10.1016/j.amc.2017.05.058

Journal Applied Mathematics and Computation Volume 318 (2018), p. 298

Model checking time-dependent system specifications using Time Stream Petri Nets and Uppaal

Franco Cicirelli, Angelo Furfaro, Libero Nigro

https://doi.org/10.1016/j.amc.2012.02.018

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8160

Modeling Infinite Games on Finite Graphs Using Numerical Infinities

Louis D’Alotto

https://doi.org/10.1007/978-3-030-93642-6_12

Book Emergence, Complexity and Computation (Numerical Infinities and Infinitesimals in Optimization) Volume 43 (2022), p. 297

Modeling of complex systems II: A minimalist and unified semantics for heterogeneous integrated systems

Boris Golden, Marc Aiguier, Daniel Krob

https://doi.org/10.1016/j.amc.2012.01.048

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8039

New Approaches to Basic Calculus: An Experimentation via Numerical Computation

Luigi Antoniotti, Fabio Caldarola, Gianfranco d’Atri, Marco Pellegrini

https://doi.org/10.1007/978-3-030-39081-5_29

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 329

Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications

Renato De Leone

https://doi.org/10.1016/j.amc.2017.03.029

Journal Applied Mathematics and Computation Volume 318 (2018), p. 290

Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications

Yaroslav D. Sergeyev

https://doi.org/10.1007/978-1-4614-7582-8_1

Book Springer Proceedings in Mathematics & Statistics (Dynamics of Information Systems: Algorithmic Approaches) Volume 51 (2013), p. 1

Numerical computations and mathematical modelling with infinite and infinitesimal numbers

Yaroslav D. Sergeyev

https://doi.org/10.1007/s12190-008-0123-7

Journal Journal of Applied Mathematics and Computing Volume 29, Issue 1-2 (2009), p. 177

Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.na.2009.02.030

Journal Nonlinear Analysis: Theory, Methods & Applications Volume 71, Issue 12 (2009), p. e1688

Observability in the Univalent Universe

Fernando Tohmé, Gianluca Caterina, Rocco Gangle

https://doi.org/10.1007/s00009-022-02121-3

Journal Mediterranean Journal of Mathematics Volume 19, Issue 5 (2022)

On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function

Yaroslav D. Sergeyev

https://doi.org/10.1134/S2070046611020051

Journal P-Adic Numbers, Ultrametric Analysis, and Applications Volume 3, Issue 2 (2011), p. 129

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

Yaroslav D. Sergeyev, Dmitri E. Kvasov, Marat S. Mukhametzhanov

https://doi.org/10.1016/j.cnsns.2017.11.013

Journal Communications in Nonlinear Science and Numerical Simulation Volume 59 (2018), p. 319

On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions

Antanas Žilinskas

https://doi.org/10.1016/j.amc.2011.07.051

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8131

On the use of the Infinity Computer architecture to set up a dynamic precision floating-point arithmetic

Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro, Francesca Mazzia

https://doi.org/10.1007/s00500-020-05220-z

Journal Soft Computing Volume 24, Issue 23 (2020), p. 17589

Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions

Fabio Caldarola, Domenico Cortese, Gianfranco d’Atri, Mario Maiolo

https://doi.org/10.1007/978-3-030-39081-5_31

Book Lecture Notes in Computer Science (Numerical Computations: Theory and Algorithms) Volume 11973 (2020), p. 358

Percolation Transition and Related Phenomena in Terms of Grossone Infinity Computations

Dmitry I. Iudin, Yaroslav D. Sergeyev

https://doi.org/10.1007/978-3-319-33924-5_11

Book Emergence, Complexity and Computation (Advances in Unconventional Computing) Volume 22 (2017), p. 239

Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming

Renato De Leone, Giovanni Fasano, Yaroslav D. Sergeyev

https://doi.org/10.1007/s10589-017-9957-y

Journal Computational Optimization and Applications Volume 71, Issue 1 (2018), p. 73

Quadratized Taylor series methods for ODE numerical integration

Alessandro Borri, Francesco Carravetta, Pasquale Palumbo

https://doi.org/10.1016/j.amc.2023.128237

Journal Applied Mathematics and Computation Volume 458 (2023), p. 128237

Rejection, Disagreement, Controversy and Acceptance in Mathematical Practice: Episodes in the Social Construction of Infinity

Paul Ernest

https://doi.org/10.1007/s10516-023-09652-8

Journal Global Philosophy Volume 33, Issue 1 (2023)

Reprint of Infinity computations in cellular automaton forest-fire model

D.I. Iudin, Ya.D. Sergeyev, M. Hayakawa

https://doi.org/10.1016/j.cnsns.2014.10.019

Journal Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 190

Single-tape and multi-tape Turing machines through the lens of the Grossone methodology

Yaroslav D. Sergeyev, Alfredo Garro

https://doi.org/10.1007/s11227-013-0894-y

Journal The Journal of Supercomputing Volume 65, Issue 2 (2013), p. 645

Solving mixed Pareto-Lexicographic multi-objective optimization problems: The case of priority chains

Leonardo Lai, Lorenzo Fiaschi, Marco Cococcioni

https://doi.org/10.1016/j.swevo.2020.100687

Journal Swarm and Evolutionary Computation Volume 55 (2020), p. 100687

Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.amc.2013.04.019

Journal Applied Mathematics and Computation Volume 219, Issue 22 (2013), p. 10668

Stochastic algorithms for solving structured low-rank matrix approximation problems

J.W. Gillard, A.A. Zhigljavsky

https://doi.org/10.1016/j.cnsns.2014.08.023

Journal Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 70

Taking the Pirahã seriously

Franco Montagna, Giulia Simi, Andrea Sorbi

https://doi.org/10.1016/j.cnsns.2014.06.052

Journal Communications in Nonlinear Science and Numerical Simulation Volume 21, Issue 1-3 (2015), p. 52

The Grossone Methodology Perspective on Turing Machines

Yaroslav D. Sergeyev, Alfredo Garro

https://doi.org/10.1007/978-3-319-09039-9_7

Book Emergence, Complexity and Computation (Automata, Universality, Computation) Volume 12 (2015), p. 139

The Olympic Medals Ranks, Lexicographic Ordering, and Numerical Infinities

Yaroslav D. Sergeyev

https://doi.org/10.1007/s00283-014-9511-z

Journal The Mathematical Intelligencer Volume 37, Issue 2 (2015), p. 4

The Sierpinski curve viewed by numerical computations with infinities and infinitesimals

Fabio Caldarola

https://doi.org/10.1016/j.amc.2017.06.024

Journal Applied Mathematics and Computation Volume 318 (2018), p. 321

The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area

Yaroslav D. Sergeyev

https://doi.org/10.1016/j.cnsns.2015.07.004

Journal Communications in Nonlinear Science and Numerical Simulation Volume 31, Issue 1-3 (2016), p. 21

The exact measures of the Sierpiński d-dimensional tetrahedron in connection with a Diophantine nonlinear system

Fabio Caldarola

https://doi.org/10.1016/j.cnsns.2018.02.026

Journal Communications in Nonlinear Science and Numerical Simulation Volume 63 (2018), p. 228

The use of grossone in Mathematical Programming and Operations Research

Sonia De Cosmis, Renato De Leone

https://doi.org/10.1016/j.amc.2011.07.042

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8029

Usage of infinitesimals in the Menger’s Sponge model of porosity

Maria C. Vita, Samuele De Bartolo, Carmine Fallico, Massimo Veltri

https://doi.org/10.1016/j.amc.2011.06.013

Journal Applied Mathematics and Computation Volume 218, Issue 16 (2012), p. 8187

Using grossone to count the number of elements of infinite sets and the connection with bijections

Maurice Margenstern

https://doi.org/10.1134/S2070046611030034

Journal P-Adic Numbers, Ultrametric Analysis, and Applications Volume 3, Issue 3 (2011), p. 196

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