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https://issues.apache.org/jira/browse/MATH-631?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13080665#comment-13080665
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Luc Maisonobe edited comment on MATH-631 at 8/7/11 9:01 PM:
------------------------------------------------------------
{quote}
The documentation says: "convergence is guaranteed". Is that false?
{quote}
It depends on what is called convergence.
If convergence is evaluated only as the best of the two endpoints (measured
along y axis), yes convergence is guaranteed and in this case it is very slow.
This is what appears in many analysis books.
If convergence is evaluated by ensuring the bracketing interval (measured along
x axis) reduces to zero (i.e. both endpoints converge to the root), convergence
is not guaranteed.
The first case is achieved with our implementation by using the function
accuracy setting. The second case is achieved with our implementation by using
relative accuracy and absolute accuracy settings, which both are computed along
x axis.
I fear that there are several different references about convergence for this
method (just as for Brent). So we already are able to implement both views.
Without any change to our implementation, we reach convergence for this example
by setting the function accuracy to 7.4e-13 or above, and it is slow (about
3500 evaluations). The default setting for function accuracy is very low
(1.0e-15) and in this case, given the variation rate of the function near the
root, it is equivalent to completely ignore convergence on y on only check the
convergence on the interval length along x.
was (Author: luc):
{quote}
The documentation says: "convergence is guaranteed". Is that false?
{quote}
It depends on what is called convergence.
If convergence is evaluated only as the best of the two endpoints, yes
convergence is guaranteed and in this case it is very slow. This is what
appears in many analysis books.
If convergence is evaluated by ensuring the bracketing interval reduces to zero
(i.e. both endpoints converge to the root), convergence is not guaranteed.
The first case is achieved with our implementation by using the function
accuracy setting. The second case is achieved with our implementation by using
relative accuracy and absolute accuracy settings, which both are computed along
x axis.
I fear that their are several different references about convergence for this
method (just as for Brent). So we already are able to implement both views.
Without any change to our implementation, we reach convergence for this example
by setting the function accuracy to 7.4e-13 or above, and it is slow (about
3500 evaluations). The default setting for function accuracy is very low
(1.0e-15) and in this case, given the variation rate of the function near the
root, it is equivalent to completely ignore convergence on y on only check the
convergence on the interval length along x.
> "RegulaFalsiSolver" failure
> ---------------------------
>
> Key: MATH-631
> URL: https://issues.apache.org/jira/browse/MATH-631
> Project: Commons Math
> Issue Type: Bug
> Reporter: Gilles
> Fix For: 3.0
>
>
> The following unit test:
> {code}
> @Test
> public void testBug() {
> final UnivariateRealFunction f = new UnivariateRealFunction() {
> @Override
> public double value(double x) {
> return Math.exp(x) - Math.pow(Math.PI, 3.0);
> }
> };
> UnivariateRealSolver solver = new RegulaFalsiSolver();
> double root = solver.solve(100, f, 1, 10);
> }
> {code}
> fails with
> {noformat}
> illegal state: maximal count (100) exceeded: evaluations
> {noformat}
> Using "PegasusSolver", the answer is found after 17 evaluations.
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