Up: Laguerre method
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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 . To find the following
scheme can be used:
A consequence of Laguerre theorem is that the best bound cannot be
lower than .
- let be such that
- let the smallest integer such that either or and
- if then substitute by such that
and go to 2