[jira] [Commented] (MATH-995) Adaptive division of segments in Quadrature Legendre-Gauss

["Ajo Fod (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/MATH-995?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13689796#comment-13689796 ] 

Ajo Fod commented on MATH-995:
------------------------------

The attached files show how to use AdaptiveQuadrature and how the existing method fails. I've wrapped the IterativeLegendreGaussIntegrator in an InfiniteIntegral object to show a specific instance of a failure of the class. The AdaptiveQuadrature object is more efficient at solving problems (in function evaluation counts) because it selectively increases resolution where the error is high. 

This problem is not limited to infinite integrals because the underlying IterativeLegendreGaussIntegrator is integrating in the region [-1,1]. 

The attached solution uses 1st and 2nd order polynomials, but it can be generalized to a higher order polynomial solutions.
                
> 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: AdaptiveQuadrature.java, InfiniteIntegral.java
>
>
> 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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