NAME

       Math::GSL::Sum - Sum series with the Levin u-transform

SYNOPSIS

           use Math::GSL::Sum qw/:all/;

           my $w = gsl_sum_levin_u_alloc(5);
           $values = [8,2,3,4,6];
           my ($status, $sum_accel, $abserr) = gsl_sum_levin_u_accel($values, 5, $w);
           gsl_sum_levin_u_free($w);

           my $w2 = gsl_sum_levin_utrunc_alloc(5);
           my ($status2, $sum_accel2, $abserr_trunc) = gsl_sum_levin_utrunc_accel($values, 5, $w2);
           gsl_sum_levin_utrunc_free($w);

DESCRIPTION

       These functions accelerate the convergence of a series using the Levin u-transform.

       •   gsl_sum_levin_u_alloc($n)

           This function allocates a workspace for a Levin u-transform of $n terms.

       •   gsl_sum_levin_u_free($w)

           - This function frees the memory associated with the workspace $w.

       •   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.

       •   gsl_sum_levin_u_minmax

       •   gsl_sum_levin_u_step

       •   gsl_sum_levin_utrunc_alloc($n)

           This function allocates a workspace for a Levin u-transform of $n terms, without error
           estimation.

       •   gsl_sum_levin_utrunc_free($w)

           This function frees the memory associated with the workspace $w.

       •   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.

       •   gsl_sum_levin_utrunc_minmax

       •   gsl_sum_levin_utrunc_step

AUTHORS

       Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

COPYRIGHT AND LICENSE

       Copyright (C) 2008-2021 Jonathan "Duke" Leto and Thierry Moisan

       This program is free software; you can redistribute it and/or modify it under the same
       terms as Perl itself.