sum.rdoc

Path: rdoc/sum.rdoc
Last Update: Sun Nov 14 14:53:48 -0800 2010

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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