Next: Implementation
Up: Budan-Fourier method
Previous: Budan-Fourier method
Contents
Budan-Fourier algorithm is a simple method which enable to determine
easily some information on the number of root of a given univariate
polynomial within a given interval. Let
the polynomial:
and
its n-th derivative. Let the interval
the
interval in which we are looking for roots. We assume that
,
and
.
We construct the sequence
from which we exclude the 0 element. Similarly we construct the
sequence
(a special treatment has to be applied for the zero element of
,
see [13]). Let
the number of change of sign
in
and
the number of change of sign in
. Then
the number of real roots of
in
, counted with their order
of multiplicity, is
or lower than this number by an even
number.
Jean-Pierre Merlet
2012-12-20