High order Brent-like bracketing solver
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Key: MATH-635
URL: https://issues.apache.org/jira/browse/MATH-635
Project: Commons Math
Issue Type: New Feature
Reporter: Luc Maisonobe
Assignee: Luc Maisonobe
Fix For: 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.
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