Analysis on the Levi-Civita field and computational applications

DOI10.1016/j.amc.2014.04.108zbMath1356.46062OpenAlexW1972496338MaRDI QIDQ299412

Khodr Shamseddine

Publication date: 22 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.04.108

zbMATH Keywords

optimizationpower seriescomputational applicationsLevi-Civita fieldsmeasure theory and integrationnon-Archimedean analysis

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Non-Archimedean valued fields (12J25) Non-Archimedean analysis (26E30)

Related Items (12)

On the analyticity of WLUD^∞ functions of one variable and WLUD^∞ functions of several variables in a complete non-Archimedean valued field ⋮ A local mean value theorem for functions on non-Archimedean field extensions of the real numbers ⋮ The Mathematical Intelligencer flunks the Olympics ⋮ Density of characters of bounded \(p\)-adic analytic functions in the topological dual ⋮ A weaker smoothness criterion for the inverse function theorem, the intermediate value theorem, and the mean value theorem in a non-Archimedean setting ⋮ On a new measure on the Levi-Civita field \(\mathcal{R}\) ⋮ On computational applications of the Levi-Civita field ⋮ Taylor's theorem, the inverse function theorem and the implicit function theorem for weakly locally uniformly differentiable functions on non-Archimedean spaces ⋮ Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem ⋮ On integrable delta functions on the Levi-Civita field ⋮ On the topological structure of a Hahn field and convergence of power series ⋮ The largest group contained in the order completion of a totally ordered group

Uses Software

• Cosy

Cites Work

• Numerical point of view on calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains
• On locally uniformly differentiable functions on a complete non-Archimedean ordered field extension of the real numbers
• Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically
• Inner product on \(B^\ast\)-algebras of operators on a free Banach space over the Levi-Civita field
• The implicit function theorem in a non-Archimedean setting
• Higher order numerical differentiation on the infinity computer
• Analytical properties of power series on Levi-Civita fields
• On the topological structure of the Levi-Civita field
• Numerical computations and mathematical modelling with infinite and infinitesimal numbers
• Fields: Algebraically closed and others
• Constrained second order optimization on non-archimedean fields
• New results on integration on the Levi-Civita field
• One-variable and multi-variable calculus on a non-Archimedean field extension of the real numbers
• Intermediate value theorem for analytic functions on a Levi-Civita field
• Modell einer Leibnizschen Differentialrechnung mit aktual unendlich kleinen Grössen sämtlicher Ordnungen
• Methodology of Numerical Computations with Infinities and Infinitesimals
• Characterization of compact and self-adjoint operators on free Banach spaces of countable type over the complex Levi-Civita field
• Computational differentiation: techniques, applications, and tools
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