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Manual Reference Pages  -  MATH::GSL::SUM (3)

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NAME

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

CONTENTS

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.
o gsl_sum_levin_u_alloc($n)

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

o gsl_sum_levin_u_free($w)

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

o 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.

o gsl_sum_levin_u_minmax
o gsl_sum_levin_u_step
o gsl_sum_levin_utrunc_alloc($n)

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

o gsl_sum_levin_utrunc_free($w)

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

o 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.

o gsl_sum_levin_utrunc_minmax
o gsl_sum_levin_utrunc_step

AUTHORS

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

COPYRIGHT AND LICENSE

Copyright (C) 2008-2011 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.

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perl v5.20.3 MATH::GSL::SUM (3) 2016-04-03

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