Type: New Feature
Affects Version/s: None
Fix Version/s: 3.0
The new bracketing solvers greatly improve usage. Unfortunately, for now there are only secant-based bracketing solvers available, and a wrapper which basically ends by adding a few secant steps to regular non-bracketing solvers.
Changing the Brent solver to provide bracket selection on the final result would depart from the standard algorithm, which is a wrong move (see
MATH-599 for a similar case recently resolved).
It would be nice to set up another solver in the same spirit as Brent (i.e. using inverse polynomial interpolation when possible and falling back to dichotomy) while retaining bracketing. A nice and simple improvement is also to use higher order inverse polynomial interpolation by retaining several previous points. This allows to build a solver that have an higher order than Newton for example but still only needs function values and no derivatives at all.