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