We consider the problem of the determination of the largest modulus of a root of a complex polynomial P. Lower and upper bounds are derived using properties of appropriate linear recurrent sequences associated to P. This allows us to give the absolute value of a dominant root as the limit in Bernoulli's process. We finally discuss a rule of Jacobi in his refinement of Bernoulli's method. Relevant examples are obtained through pari and maple procedures.
Publié le : 2001-06-18
Classification:
linear recurrent sequence,
Bernoulli's method,
"linear recurrent sequence,
dominant root,
Bernoulli's method",
11B37, 68W30,30C10,26C05,
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
@article{hal-00129667,
author = {Mignotte, Maurice and Stefanescu, Doru},
title = {Linear Recurrent Sequences and Polynomial Roots},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129667}
}
Mignotte, Maurice; Stefanescu, Doru. Linear Recurrent Sequences and Polynomial Roots. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129667/