In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind:
| +1 | |
| \int | |
| -1 |
| f(x) | |
| \sqrt{1-x2 |
}dx
and
| +1 | |
| \int | |
| -1 |
\sqrt{1-x2}g(x)dx.
In the first case
| +1 | |
| \int | |
| -1 |
| f(x) | |
| \sqrt{1-x2 |
}dx ≈
| n | |
| \sum | |
| i=1 |
wif(xi)
where
xi=\cos\left(
| 2i-1 | |
| 2n |
\pi\right)
and the weight
wi=
| \pi | |
| n |
.
In the second case
| +1 | |
| \int | |
| -1 |
\sqrt{1-x2}g(x)dx ≈
| n | |
| \sum | |
| i=1 |
wig(xi)
where
xi=\cos\left(
| i | |
| n+1 |
\pi\right)
and the weight
wi=
| \pi | |
| n+1 |
\sin2\left(
| i | |
| n+1 |
\pi\right).