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https://github.com/JuliaApproximation/FastGaussQuadrature.jl

Julia package for Gaussian quadrature
https://github.com/JuliaApproximation/FastGaussQuadrature.jl

gauss-quadrature julia numerical-integration

Last synced: about 2 months ago
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Julia package for Gaussian quadrature

Host: GitHub
URL: https://github.com/JuliaApproximation/FastGaussQuadrature.jl
Owner: JuliaApproximation
License: mit
Created: 2014-08-31T14:35:16.000Z (almost 10 years ago)
Default Branch: master
Last Pushed: 2024-01-13T12:16:33.000Z (6 months ago)
Last Synced: 2024-05-19T06:01:35.487Z (about 2 months ago)
Topics: gauss-quadrature, julia, numerical-integration
Language: Julia
Homepage: https://juliaapproximation.github.io/FastGaussQuadrature.jl/stable/
Size: 1.06 MB
Stars: 293
Watchers: 21
Forks: 42
Open Issues: 13
Metadata Files:
- Readme: README.md
- License: LICENSE

Lists

awesome-sciml - JuliaApproximation/FastGaussQuadrature.jl: Julia package for Gaussian quadrature

README

        FastGaussQuadrature.jl

=========

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaApproximation.github.io/FastGaussQuadrature.jl/stable)

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://JuliaApproximation.github.io/FastGaussQuadrature.jl/dev)

[![Build Status](https://github.com/JuliaApproximation/FastGaussQuadrature.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/FastGaussQuadrature.jl/actions)

[![codecov](https://codecov.io/gh/JuliaApproximation/FastGaussQuadrature.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/FastGaussQuadrature.jl)

[![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)

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](http://www.chebfun.org).

An introduction to Gauss quadrature can be found [here](http://en.wikipedia.org/wiki/Gaussian_quadrature).

For a quirky account on the history of computing Gauss-Legendre quadrature, see [[6]](http://pi.math.cornell.edu/~ajt/papers/QuadratureEssay.pdf).

## 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

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

```