Displaying similar documents to “Characterization of optimal polynomial and rational starting approximations”

Niven’s Theorem

Artur Korniłowicz, Adam Naumowicz (2016)

Formalized Mathematics

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This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9].

A new rational and continuous solution for Hilbert's 17th problem.

Charles N. Delzell, Laureano González-Vega, Henri Lombardi (1992)

Extracta Mathematicae

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In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is...