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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-27 9:38 |
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Conference: Bucharest University Faculty of Physics 2017 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
Efficiency of the bound R+r of Lagrange
Authors:
Prashant BATRA (1), Doru STEFANESCU (2)
Affiliation:
1) Hamburg University of Technology, Institute for Reliable Computing
2) University of Bucharest, Faculty of Physics
E-mail
doru.stefanescu@gmail.com
Keywords:
polynomial roots, Lagrange's bound.
Abstract:
Let F(X) = X^d + a_1X^(d-1) + ... + a_d be a polynomial with real coefficients. Lagrange stated that a bound for the positive roots is given by the nmber R+r, where R and r are the largest numbers in the sequence (|a_i|^(1/i)). We obtain a refinement of this result and study its efficiency. The proofs are based on the following Theorem: The the largest positive root of the polynomial u(X)=(X−2r)X^j −(R^j − ρ^j )(X − ρ) is an upper bound for the absolute values of the roots of the polynomial F.
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