Adaptive 1d numerical Gauss–Kronrod integration in Julia
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Started In
December 2016


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This package provides support for one-dimensional numerical integration in Julia using adaptive Gauss-Kronrod quadrature. The code was originally part of Base Julia. It supports integration of arbitrary numeric types, including arbitrary precision (BigFloat), and even integration of arbitrary normed vector spaces (e.g. matrix-valued integrands).

The package provides three basic functions: quadgk, gauss, and kronrod. quadgk performs the integration, gauss computes Gaussian quadrature points and weights for integrating over the interval [a, b], and kronrod computes Kronrod points, weights, and embedded Gaussian quadrature weights for integrating over [-1, 1]. Typical usage looks like:

using QuadGK
integral, err = quadgk(x -> exp(-x^2), 0, 1, rtol=1e-8)

which computes the integral of exp(–x²) from x=0 to x=1 to a relative tolerance of 10⁻⁸, and returns the approximate integral = 0.746824132812427 and error estimate err = 7.887024366937112e-13 (which is actually smaller than the requested tolerance: convergence was very rapid because the integrand is smooth).

For more information, see the documentation.