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From "Gilles (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-995) Adaptive division of segments in Quadrature Legendre-Gauss
Date Thu, 11 Jul 2013 21:09:49 GMT

    [ https://issues.apache.org/jira/browse/MATH-995?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13706230#comment-13706230
] 

Gilles commented on MATH-995:
-----------------------------

bq. [...] if the IterativeGaussLegendreIntegrator is retained in the codebase [...]

It is not the only instance where CM contains an algorithm that has shortcomings or drawbacks.
Not every condition that leads to (numerical) problems can be easily characterized, short
of seeing that the result is incorrect.
[I recall a discussion about the "Regula falsi" root solver where the algorithm was stuck
in an infinite loop; in that case it was possible to cheaply test for the condition and throw
an exception.]

The Javadoc now draws attention that the algorithm is not 100% fool-proof.

                
> Adaptive division of segments in Quadrature  Legendre-Gauss
> -----------------------------------------------------------
>
>                 Key: MATH-995
>                 URL: https://issues.apache.org/jira/browse/MATH-995
>             Project: Commons Math
>          Issue Type: Bug
>            Reporter: Ajo Fod
>         Attachments: gaussian__sigma_1000.png, gaussian__sigma_1000_zoom.png, gaussian__sigma_1.png,
patch-code, patch-code, patch-code, patch-test
>
>
> I think the existing Legendre-Gauss object fails for certain integrals. An example of
failure and a solution that divides segments based on error is provided. Please let me know
if I'm not using the Legendre-Gauss object correctly.

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