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Non-Archimedean Analysis and Rigorous Computation

Abstract

An introduction to recent work on analysis over the nonarchimedean Levi-Civita field related to applications for common numerical tasks is provided. After studying the algebraic, order, and topological properties, a calculus is developed under which central concepts like the intermediate value theorem, mean value theorem, and Taylor’s theorem with remainder hold under slightly stronger conditions. Most importantly for practical applications, it allows the computation of derivatives of real functions as difference quotients with infinitesimal increment.

M. Berz, International Journal of Applied Mathematics 2(5) (2000) 889-930

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