منابع مشابه
Global Newton Iteration over Archimedean and non-Archimedean Fields
In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...
متن کاملOne-dimensional Optimization on Non-archimedean Fields
One dimensional optimization on non-Archimedean fields is presented. We derive first and second order necessary and sufficient optimality conditions. For first order optimization, these conditions are similar to the corresponding real ones; but this is not the case for higher order optimization. This is due to the total disconnectedness of the given non-Archimedean field in the order topology, ...
متن کاملA Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields
In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...
متن کاملIntermediate Values and Inverse Functions on Non-archimedean Fields
Continuity or even differentiability of a function on a closed interval of a non-Archimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness of the field in the order topology. In this paper, we show that differentiability (in the topologica...
متن کاملNontrivial order preserving automorphisms of non-Archimedean fields
A study of order preserving field automorphisms of ordered nonArchimedean field extensions of R will be presented. We show that, while the identity map is the only field automorphism of R, infinitely many nontrivial order preserving field automorphisms can be constructed on an ordered nonArchimedean field extension F of R. Moreover, we show that if P is an order preserving field automorphism of...
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ژورنال
عنوان ژورنال: Annales mathématiques Blaise Pascal
سال: 1995
ISSN: 1259-1734
DOI: 10.5802/ambp.30