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Axel Kramer commented on MATH599:

I used the new RegulaFalsi implementation in my project
http://code.google.com/p/symja/wiki/UsedLibraries#CommonsMath_functions
for the FindRoot function.
The call:
FindRoot[Exp[x]==Pi^3,{x,1,10}, RegulaFalsi]
seems to run endlessly?
For the other Solvers the method stops very quick.
Shouldn't there be a test for a "maximum iteration" in the while loop of the BaseSecantSolver#doSolve()
method()?
> Reimplementation of Secantbased root finding algorithms
> 
>
> Key: MATH599
> URL: https://issues.apache.org/jira/browse/MATH599
> Project: Commons Math
> Issue Type: Improvement
> Reporter: Dennis Hendriks
> Labels: documentation, patch
> Fix For: 3.0
>
> Attachments: secantbasedrootfindingalgos.patch, secantbasedrootfindingalgos2.patch,
secantbasedrootfindingalgos2.zip
>
>
> Apache Commons Math currently has a SecantSolver. It is unclear exactly what algorithm
this solver implements. It states: "The algorithm is modified to maintain bracketing of a
root by successive approximations. Because of forced bracketing, convergence may be slower
than the unrestricted Secant algorithm. However, this implementation should in general outperform
the Regula Falsi method." The Regula Falsi method is exactly the Secant method modified to
maintain a bracketed solution. It is therefore unclear what other modifications were done
to make it 'better' than the Regula Falsi method.
> Besides the Secant and Regula Falsi methods, several other Secantbased rootfinding
algorithms exist, such as the the Illinois method, and the Pegasus method. All 4 are wellknown,
publisched algorithms.
> I created a patch, which changes the following:
>  Removed SecantSolver rootfinding algorithm.
>  Implemented new Secantbased rootfinding algorithms: SecantSolver, RegulaFalsiSolver,
IllinoisSolver, and PegasusSolver.
>  Introduced BracketedSolution interface and AllowedSolutions enumeration, to control
allowed solutions (underapproximations and overapproximations) for bracketed rootfinding
algorithms. Implemented for RegulaFalsiSolver, IllinoisSolver, and PegasusSolver.
>  Fixed documentation of BaseUnivariateRealSolver.solve methods, such that documentation
order of arguments matches the order of the actual arguments.
> Note that the original SecantSolver was removed, and replaced by a rootfinding algorithm
that actually implements the Secant rootfinding algorithm. As such, existing code using the
SecantSolver is not backwards compatible. That is, even though the new SecantSolver does implement
the same interfaces, the rootfinding solutions may differ. In particular, the new SecantSolver
does not maintain a bracketed solution, and does not guarantee convergence.
> I added unit tests, and I did a build, including checkstyle checking. I did not fix all
checkstyle warnings though, as I consider some of them false positives.

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