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On an estimation of polynomial roots by Lagrange
Mignotte, Maurice ; Stefanescu, Doru
HAL, hal-00129675 / Harvested from HAL
Text on HAL
"Lagrange stated the following inequality: An upper bound forthe positive real roots of a monic polynomial over $R$ is equal to$R+ho$, where $R$ and $ho$ are the two largest numbers in the sethbox{${sqrt[j]{|a_j|}; ,jin J}$, where ${a_j; ,jin J}$ }are the negative coefficients. Since Lagrange does not provide a complete proof, wegive one following Cauchy's method. We also present a slightgeneralization of this theorem of Lagrange, using a result ofKojima."
Publié le : 2002-05-17
Classification:  Polynomial roots,  bound of Lagrange,  "Polynomial roots,  bound of Lagrange",  30C10, 12D10,26C05,  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 
@article{hal-00129675,
     author = {Mignotte, Maurice and Stefanescu, Doru},
     title = {On an estimation of polynomial roots by Lagrange},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129675}
}

Mignotte, Maurice; Stefanescu, Doru. On an estimation of polynomial roots by Lagrange. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129675/