Chebyshev–Gauss quadrature
In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind:
and
In the first case
where
and the weight
- [1]
In the second case
where
and the weight
- [2]
See also
- Chebyshev polynomials
- Chebyshev nodes
References
- ^ Abramowitz, M & Stegun, I A, Handbook of Mathematical Functions, 10th printing with corrections (1972), Dover, ISBN 978-0-486-61272-0. Equation 25.4.38.
- ^ Abramowitz, M & Stegun, I A, Handbook of Mathematical Functions, 10th printing with corrections (1972), Dover, ISBN 978-0-486-61272-0. Equation 25.4.40.
External links
- Chebyshev-Gauss Quadrature from Wolfram MathWorld
- Gauss–Chebyshev type 1 quadrature and Gauss–Chebyshev type 2 quadrature, free software in C++, Fortran, and Matlab.
- v
- t
- e
Numerical integration
- Trapezoidal rule
- Simpson's rule
- Simpson's 3/8 rule
- Adaptive Simpson's method
- Boole's rule
- Romberg's method