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FastGaussQuadrature

Julia package for Gaussian quadrature

Readme

FastGaussQuadrature.jl

Stable Dev Build Status codecov

A Julia package to compute n-point Gauss quadrature nodes and weights to 16-digit accuracy and in O(n) time. So far the package includes gausschebyshev(), gausslegendre(), gaussjacobi(), gaussradau(), gausslobatto(), gausslaguerre(), and gausshermite(). This package is heavily influenced by Chebfun.

An introduction to Gauss quadrature can be found here. For a quirky account on the history of computing Gauss-Legendre quadrature, see [6].

Our Aims

  • The fastest Julia code for Gauss quadrature nodes and weights (without tabulation).
  • Change the perception that Gauss quadrature rules are expensive to compute.

Example usage

julia> @time nodes, weights = gausslegendre( 100000 );
  0.002192 seconds (10 allocations: 2.289 MiB)

# integrates f(x) = x^2 from -1 to 1
julia> @time dot( weights, nodes.^2 )
  0.000184 seconds (7 allocations: 781.422 KiB)
0.6666666666666665

First Commit

08/31/2014

Last Touched

10 days ago

Commits

231 commits