A Simulink-Based Infinity Computer Simulator and Some Applications

DOI10.1007/978-3-030-40616-5_31OpenAlexW3006576224MaRDI QIDQ5122312

Alberto Falcone, Marat S. Mukhametzhanov, Alfredo Garro, Yaroslav D. Sergeyev

Publication date: 22 September 2020

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-40616-5_31

zbMATH Keywords

numerical differentiationscientific computingInfinity Computer

Mathematics Subject Classification ID

Numerical analysis (65-XX)

Related Items (9)

Simulation of hybrid systems under Zeno behavior using numerical infinitesimals ⋮ On the use of the infinity computer architecture to set up a dynamic precision floating-point arithmetic ⋮ On the topological convergence of multi-rule sequences of sets and fractal patterns ⋮ Spherical separation with infinitely far center ⋮ Iterative grossone-based computation of negative curvature directions in large-scale optimization ⋮ Novel local tuning techniques for speeding up one-dimensional algorithms in expensive global optimization using Lipschitz derivatives ⋮ The big-M method with the numerical infinite \(M\) ⋮ A Simulink-based software solution using the infinity computer methodology for higher order differentiation ⋮ Non-Archimedean zero-sum games

Cites Work

• Numerical point of view on calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains
• Higher order numerical differentiation on the infinity computer
• Planar methods and grossone for the conjugate gradient breakdown in nonlinear programming
• Conjugate-symplecticity properties of Euler-Maclaurin methods and their implementation on the infinity computer
• On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales
• A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic
• Numerical infinities and infinitesimals: methodology, applications, and repercussions on two Hilbert problems
• Nonlinear programming and grossone: quadratic programing and the role of constraint qualifications
• Lexicographic multi-objective linear programming using grossone methodology: theory and algorithm
• Numerical infinitesimals in a variable metric method for convex nonsmooth optimization
• A Study of Mathematical Determination through Bertrand’s Paradox
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