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.