[Bug-gsl] [bug #32233] Gauss-Legendre routine does not work in gsl-1.14

[Jussi Lehtola]

URL:
  <http://savannah.gnu.org/bugs/?32233>

                 Summary: Gauss-Legendre routine does not work in gsl-1.14
                 Project: GNU Scientific Library
            Submitted by: jussilehtola
            Submitted on: Mon 24 Jan 2011 03:06:59 PM GMT
                Category: None
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

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Details:

The Gauss-Legendre routines are not working in gsl-1.14.

According to the documentation, gsl_integration_glfixed_table_alloc should
compute the abscissae and weights for the wanted order of integration.

However, at least the weights are clearly wrong. The sum of the weights
should always give the length of the integration interval [1], which is not
the case with the routine.

For instance, the 2nd order result computed by
gsl_integration_glfixed_table_alloc is

Gauss-Legendre abscissae and weights of order 2, sum of weights 1.000000e+00,
precomputed? 1
        x               w
        5.773503e-01    1.000000e+00
        1.000000e+00    0.000000e+00

so the first point is calculated correctly; the second should be at
-5.773503e-01 with a weight also of 1.000000e+00.

[1] http://mathworld.wolfram.com/Legendre-GaussQuadrature.html



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File Attachments:


-------------------------------------------------------
Date: Mon 24 Jan 2011 03:06:59 PM GMT  Name: legendretest.c  Size: 1kB   By:
jussilehtola

<http://savannah.gnu.org/bugs/download.php?file_id=22503>

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