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From "Dennis Hendriks (JIRA)" <>
Subject [jira] [Updated] (MATH-599) Re-implementation of Secant-based root finding algorithms
Date Thu, 23 Jun 2011 09:06:52 GMT


Dennis Hendriks updated MATH-599:


New test, with output for both dense and non-dense step handler.

Note how for the non-dense step handler, the derivatives are computed for 10.0, and the result
is 24.999999999999996. It then continues to call the step handler for time 10.0 with value
21.35298598981348, which is the value calculated for time 8.784328663271161, from before the
previous time the step handler was called. It seems the compute derivative method is called
for the appropriate times, only the output is not correctly used to set the interpolator values.

If you think this is indeed *only* caused by the optionality of dense output, or it is no
longer relevant if non-dense output is removed, then removing the non-dense option would indeed
fix this issue.

It would probably be better to create a separate issue for the removal of non-dense output.
I have no objections to the removal of non-dense output.

> Re-implementation of Secant-based root finding algorithms
> ---------------------------------------------------------
>                 Key: MATH-599
>                 URL:
>             Project: Commons Math
>          Issue Type: Improvement
>            Reporter: Dennis Hendriks
>              Labels: documentation, patch
>             Fix For: 3.0
>         Attachments: secant-based-root-finding-algos.patch, secant-based-root-finding-algos2.patch,
> 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 Secant-based root-finding
algorithms exist, such as the the Illinois method, and the Pegasus method. All 4 are well-known,
publisched algorithms.
> I created a patch, which changes the following:
>  - Removed SecantSolver root-finding algorithm.
>  - Implemented new Secant-based root-finding algorithms: SecantSolver, RegulaFalsiSolver,
IllinoisSolver, and PegasusSolver.
>  - Introduced BracketedSolution interface and AllowedSolutions enumeration, to control
allowed solutions (under-approximations and over-approximations) for bracketed root-finding
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 root-finding algorithm
that actually implements the Secant root-finding 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 root-finding 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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