Chebyshev–Gauss quadrature - Alchetron, the free social encyclopedia

In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind:

∫ − 1 + 1 f ( x ) 1 − x 2 d x

and

∫ − 1 + 1 1 − x 2 g ( x ) d x .

In the first case

∫ − 1 + 1 f ( x ) 1 − x 2 d x ≈ ∑ i = 1 n w i f ( x i )

where

x i = cos ⁡ ( 2 i − 1 2 n π )

and the weight

w i = π n .

In the second case

∫ − 1 + 1 1 − x 2 g ( x ) d x ≈ ∑ i = 1 n w i g ( x i )

where

x i = cos ⁡ ( i n + 1 π )

and the weight

w i = π n + 1 sin 2 ⁡ ( i n + 1 π ) .

References

Chebyshev–Gauss quadrature Wikipedia

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