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Clean up Sum POD

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1 parent 06f5fa4 commit b382874babb761edd13a3dd02ef55782939b3611 @leto committed Oct 13, 2011
Showing with 39 additions and 8 deletions.
  1. +39 −8 pod/Sum.pod
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@@ -17,7 +17,7 @@ __END__
=head1 NAME
-Math::GSL::Sum - Functions to accelerate the convergence of a series using the Levin u-transform.
+Math::GSL::Sum - Sum series with the Levin u-transform
=head1 SYNOPSIS
@@ -34,25 +34,56 @@ Math::GSL::Sum - Functions to accelerate the convergence of a series using the L
=head1 DESCRIPTION
-Here is a list of all the functions included in this module :
+These functions accelerate the convergence of a series using the Levin u-transform.
=over
-=item * gsl_sum_levin_u_alloc($n) - This function allocates a workspace for a Levin u-transform of $n terms.
+=item * gsl_sum_levin_u_alloc($n)
-=item * gsl_sum_levin_u_free($w) - This function frees the memory associated with the workspace $w.
+This function allocates a workspace for a Levin u-transform of $n terms.
-=item * gsl_sum_levin_u_accel($array, $array_size, $w) - This function takes the terms of a series in the array reference $array of size $array_size and computes the extrapolated limit of the series using a Levin u-transform. Additional working space must be provided in $w. The function returns multiple values in this order : 0 if the operation succeeded, 1 otherwise, the extrapolated sum and an estimate of the absolute error. The actual term-by-term sum is returned in $w->{sum_plain}. The algorithm calculates the truncation error (the difference between two successive extrapolations) and round-off error (propagated from the individual terms) to choose an optimal number of terms for the extrapolation. All the terms of the series passed in through array should be non-zero.
+=item * gsl_sum_levin_u_free($w)
+
+- This function frees the memory associated with the workspace $w.
+
+=item * gsl_sum_levin_u_accel($array, $array_size, $w)
+
+This function takes the terms of a series in the array reference $array of size
+$array_size and computes the extrapolated limit of the series using a Levin
+u-transform. Additional working space must be provided in $w. The function
+returns multiple values in this order : 0 if the operation succeeded, 1
+otherwise, the extrapolated sum and an estimate of the absolute error. The
+actual term-by-term sum is returned in $w->{sum_plain}. The algorithm
+calculates the truncation error (the difference between two successive
+extrapolations) and round-off error (propagated from the individual terms) to
+choose an optimal number of terms for the extrapolation. All the terms of the
+series passed in through array should be non-zero.
=item * gsl_sum_levin_u_minmax
=item * gsl_sum_levin_u_step
-=item * gsl_sum_levin_utrunc_alloc($n) - This function allocates a workspace for a Levin u-transform of $n terms, without error estimation.
+=item * gsl_sum_levin_utrunc_alloc($n)
+
+This function allocates a workspace for a Levin u-transform of $n terms,
+without error estimation.
+
+=item * gsl_sum_levin_utrunc_free($w)
+
+This function frees the memory associated with the workspace $w.
-=item * gsl_sum_levin_utrunc_free($w) - This function frees the memory associated with the workspace $w.
+=item * gsl_sum_levin_utrunc_accel($array, $array_size, $w)
-=item * gsl_sum_levin_utrunc_accel($array, $array_size, $w) - This function takes the terms of a series in the array reference $array of size $array_size and computes the extrapolated limit of the series using a Levin u-transform. Additional working space must be provided in $w. The function returns multiple values in this order : 0 if the operation succeeded, 1 otherwise, the extrapolated sum and an estimate of the error. The actual term-by-term sum is returned in $w->{sum_plain}. The algorithm terminates when the difference between two successive extrapolations reaches a minimum or is sufficiently small. To improve the reliability of the algorithm the extrapolated values are replaced by moving averages when calculating the truncation error, smoothing out any fluctuations.
+This function takes the terms of a series in the array reference $array of size
+$array_size and computes the extrapolated limit of the series using a Levin
+u-transform. Additional working space must be provided in $w. The function
+returns multiple values in this order : 0 if the operation succeeded, 1
+otherwise, the extrapolated sum and an estimate of the error. The actual
+term-by-term sum is returned in $w->{sum_plain}. The algorithm terminates when
+the difference between two successive extrapolations reaches a minimum or is
+sufficiently small. To improve the reliability of the algorithm the
+extrapolated values are replaced by moving averages when calculating the
+truncation error, smoothing out any fluctuations.
=item * gsl_sum_levin_utrunc_minmax

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