`quadgk`

Adaptive Gauss-Kronrod quadrature, including infinite limits and singular endpoints.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

q = quadgk(fun, a, b)

Integrates fun from a to b.

[q, errbnd] = quadgk(fun, a, b)

Also returns an estimate of the error.

q = quadgk(fun, a, b, Name, Value)

Sets options such as 'AbsTol', 'RelTol' and 'Waypoints'.

Description

Infinite limits are mapped to a finite interval, and endpoint singularities of the type 1/sqrt(x) are tamed by a change of variables, which makes the method robust. A contour can be defined in the complex plane through complex waypoints.

integral is built on the same algorithm and is generally preferred in new code.

Input arguments

fun: Handle accepting a vector x and returning a vector.
a, b: Limits, which may be infinite.
'Waypoints': Interior points at which to split the interval, for integrands with kinks or discontinuities.

Output arguments

q: Approximate value of the integral.
errbnd: Estimated upper bound on the absolute error.

Example

An integrable singularity

q = quadgk(@(x) 1./sqrt(x), 0, 1)
quadgk(@(x) exp(-x.^2), -Inf, Inf)

Output

q = 2.0000
ans = 1.7725

quadgk