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

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
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
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
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
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
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
AIP Conference Proceedings
Louis D’Alotto
https://doi.org/10.1063/1.4965309
Conference:  AIP Conference Proceedings Volume 1776 (2016), p. 020003
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
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
AIP Conference Proceedings
F. Mazzia, Ya. D. Sergeyev, F. Iavernaro, P. Amodio, M. S. Mukhametzhanov
https://doi.org/10.1063/1.4965397
Conference:  AIP Conference Proceedings Volume 1776 (2016), p. 090033
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
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
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
AIP Conference Proceedings
Yaroslav D. Sergeyev
https://doi.org/10.1063/1.5043649
Conference:  AIP Conference Proceedings Volume 1978 (2018), p. 020004
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
AIP Conference Proceedings
Yaroslav D. Sergeyev
https://doi.org/10.1063/1.4951756
Conference:  AIP Conference Proceedings Volume 1738 (2016), p. 020012
AIP Conference Proceedings
Claudia Roberta Calidonna, Salvatore Di Gregorio, Francesco Gullace, Daniel Gullì, Valeria Lupiano
https://doi.org/10.1063/1.4952339
Conference:  AIP Conference Proceedings Volume 1738 (2016), p. 480103
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 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
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
AIP Conference Proceedings
Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev
https://doi.org/10.1063/1.4965404
Conference:  AIP Conference Proceedings Volume 1776 (2016), p. 090040
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
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
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
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
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
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 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 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
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 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
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 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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