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