Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
A subrecursive refinement of the fundamental theorem of algebra

Speaker: Peter Peshev
Author(s): Peter Peshev and Dimiter Skordev
Presentation: FTA20MIN.pdf
Slot: Tue, 15:10-15:30, Faraday D (col. 4)

Abstract

A proof by P. C. Rosenbloom of the fundamental theorem of algebra is used in the paper for obtaining a subrecursive refinement of the theorem. Arbitrary complex numbers are supposed to be represented as limits of such sequences of rational ones that the distance between the n-th term of the sequence and its limit is not greater than the reciprocal of n+1. In the case when polynomials of a fixed degree are considered, we show the existence of computable operators that belong to the second Grzegorczyk class and transform any representations of the coefficients of any monic polynomial into representations of its roots.


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