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# Series Acceleration

In Ruby/GSL, series acceleration functions are provided as singleton methods for the `GSL::Sum::Levin_u, Levin_utrunc` classes, and methods of an object of the GSL::Vector class.

## Modules and classes

- GSL

  - Sum (Module)

    - Levin_u (Class)

    - Levin_utrunc (Class)

## Methods

- GSL::Sum::Levin_u.alloc(size)

- GSL::Sum::Levin_utrunc.alloc(size)

- GSL::Sum::Levin_u.accel(v)

  This method takes the terms of a series in vector `v` and computes the extrapolated limit of the series using a Levin u-transform. This returns an array of `[sum, abserr, sum_plain, terms_used]`, where `sum` is the extrapolated sum, `abserr` is an estimate of the absolute error, and `sum_plain` is the actual term-by-term sum.

- GSL::Sum::Levin_utrunc.accel(v)

  This method takes the terms of a series in vector `v` and computes the extrapolated limit of the series using a Levin u-transform. This returns an array of `[sum, abserr_trunc, sum_plain, terms_used]`.

- GSL::Sum::Levin_u#accel(v)

- GSL::Sum::Levin_u#sum_plain

- GSL::Sum::Levin_u#terms_used

- GSL::Sum::Levin_utrunc#accel(v)

- GSL::Sum::Levin_utrunc#sum_plain

- GSL::Sum::Levin_utrunc#terms_used

- GSL::Vector#accel

- GSL::Vector#accel_sum

- GSL::Vector#sum_accel

- GSL::Vector#sum

  These calculate the "extrapolated" sum of the terms contained in a GSL::Vector object, using a Levin u-transform. The returned values is a Ruby array with 4 elements, as [`sum_accel, err, sum_plain, terms_used`], where `sum_accel` is the extraplated sum, `err` is the absolute error, `sum_plain` is the term-by-term sum, and `terms_used` is the number of terms actually used in the calculation.

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