Analysis on the Levi-Civita field and computational applications
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Publication:299412
DOI10.1016/j.amc.2014.04.108zbMath1356.46062OpenAlexW1972496338MaRDI QIDQ299412
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
optimizationpower seriescomputational applicationsLevi-Civita fieldsmeasure theory and integrationnon-Archimedean analysis
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
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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