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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