Numerical Quadrature (integration)
Numerical integration — the numerical evaluation of an integral
- Rectangle method — first-order method, based on (piecewise) constant approximation
- Trapezoidal rule — second-order method, based on (piecewise) linear approximation
- Simpson's rule — fourth-order method, based on (piecewise) quadratic approximation
- Adaptive Simpson's method
- Boole's rule — sixth-order method, based on the values at five equidistant points
- Newton–Cotes formulas — generalizes the above methods
- Romberg's method — Richardson extrapolation applied to trapezium rule
- Gaussian quadrature — highest possible degree with given number of points
- Chebyshev–Gauss quadrature — extension of Gaussian quadrature for integrals with weight (1 − x2)±1/2 on
- Gauss–Hermite quadrature — extension of Gaussian quadrature for integrals with weight exp(−x2) on
- Gauss–Jacobi quadrature — extension of Gaussian quadrature for integrals with weight (1 − x)α (1 + x)β on
- Gauss–Laguerre quadrature — extension of Gaussian quadrature for integrals with weight exp(−x2) on
- Gauss–Kronrod quadrature formula — nested rule based on Gaussian quadrature
- Gauss–Kronrod rules
- Tanh-sinh quadrature — variant of Gaussian quadrature which works well with singularities at the end points
- Clenshaw–Curtis quadrature — based on expanding the integrand in terms of Chebyshev polynomials
- Adaptive quadrature — adapting the subintervals in which the integration interval is divided depending on the integrand
- Monte Carlo integration — takes random samples of the integrand
- See also #Monte Carlo method
- Lebedev quadrature — uses a grid on a sphere with octahedral symmetry
- Sparse grid
- Coopmans approximation
- Numerical differentiation — for fractional-order integrals
- Numerical smoothing and differentiation
- Adjoint state method — approximates gradient of a function in an optimization problem
- Euler–Maclaurin formula
Read more about this topic: List Of Numerical Analysis Topics
Famous quotes containing the word numerical:
“The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.”
—Ralph Waldo Emerson (1803–1882)