Speaker: Imme van den Berg (CIMA, Universidade de Évora).

Abstract: Uncertainties and imprecisions in measurement and calculation are modelled within nonstandard analysis. The approach is asymptotic, taking profit of the existence of infinitesimals and of a large hierarchy of orders of magnitude within the infinitesimals. We do not use groups of functions, like Oh’s and oh’s, but convex groups of real numbers, so-called (scalar) neutrices. They obey algebraic laws not unlike the laws of the real number system itself, modelling error propagation. We study systems of linear equations, treating imprecisions individually by neutrices, both in the coefficients and the right-hand side. The algebraic laws are strong enough for defining the usual concepts of linear algebra and applying general solution methods, like Gauss-Jordan elimination and Cramer’s rule. Solution sets are intermediate between points and linear subspaces, based on neutrices with a well-defined higher dimension.

Joint work with Nam Van Tran, Ho Chi Min City University of Technology and Education, Vietnam, and Júlia Justino, Instituto Politécnico de Setubal.

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