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) 2008-2024 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.

perl v5.40.0                                       2024-10-20                                Math::GSL::Sum(3pm)