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From "Luc Maisonobe (Commented) (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-716) BracketingNthOrderBrentSolver exceeds maxIterationCount while updating always the same boundary
Date Thu, 01 Dec 2011 22:16:40 GMT

    [ https://issues.apache.org/jira/browse/MATH-716?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13161241#comment-13161241
] 

Luc Maisonobe commented on MATH-716:
------------------------------------

The following simple test reproduces the bad behavior with a trivial function:
{code}
    @Test
    public void testIssue716() {
        BracketingNthOrderBrentSolver solver =
                new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-10, 0.0, 5);
        UnivariateFunction sharpTurn = new UnivariateFunction() {
            public double value(double x) {
                return (2 * x + 1) / (1.0e9 * (x + 1));
            }
        };
        double result = solver.solve(100, sharpTurn, -0.9999999, 30, 15, AllowedSolution.RIGHT_SIDE);
        Assert.assertEquals(0, sharpTurn.value(result), solver.getFunctionValueAccuracy());
        Assert.assertTrue(sharpTurn.value(result) >= 0);
        Assert.assertEquals(-0.5, result, 1.0e-10);
    }
{code}
The test fails with TooManyEvaluationsException. In fact, only the right side of the bracketing
interval is updated and very slowly decreases from 15.0 to 14.999677603318897 while the left
side of the bracketing interval is stuck at -0.9999999.
                
> BracketingNthOrderBrentSolver exceeds maxIterationCount while updating always the same
boundary
> -----------------------------------------------------------------------------------------------
>
>                 Key: MATH-716
>                 URL: https://issues.apache.org/jira/browse/MATH-716
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>            Reporter: Pascal Parraud
>            Assignee: Luc Maisonobe
>            Priority: Minor
>
> In some cases, the aging feature in BracketingNthOrderBrentSolver fails.
> It attempts to balance the bracketing points by targeting a non-zero value instead of
the real root. However, the chosen target is too close too zero, and the inverse polynomial
approximation is always on the same side, thus always updates the same bracket.
> In the real used case for a large program, I had a bracket point xA = 12500.0, yA = 3.7e-16,
agingA = 0, which is the (really good) estimate of the zero on one side of the root and xB
= 12500.03, yB = -7.0e-5, agingB = 97. This shows that the bracketing interval is completely
unbalanced, and we never succeed to rebalance it as we always updates (xA, yA) and never updates
(xB, yB).

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