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Let
be an univariate polynomial of degree
:
with
,
.
Let's define the sequence :
If it exists a real
such that
for all
in
[0,
], then
for all
. Consequently all the roots of
are lower than
[13]. To find
the following
scheme can be used:
- let
be such that
- let
the smallest integer such that either
or
and
- if
then substitute
by
such that
and go to 2
- return
A consequence of Laguerre theorem is that the best bound cannot be
lower than
.
Jean-Pierre Merlet
2012-12-20