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Brent method is an iterative scheme used to obtain one root of the
equation
within an interval
. It assumes that
. Let
be the mid-point of the interval
. A new estimate of the root is
with:
with:
In this method
is considered to be the current estimate of the
solution. The term
is a correction factor: when this factor
leads to a new estimate of the solution outside the interval we use a
bisection method to compute a new interval
. In other words
if
the new interval is
and if
the new interval is
. Therefore Brent
method is a cross between a bisection method and a super-linear method
which insure that the estimate of the solution always lie within the
interval
.
Jean-Pierre Merlet
2012-12-20