Gaussian Quadrature

Gaussian quadrature is a numerical integration technique used to approximate definite integrals of functions. It involves selecting a set of points (nodes) and their corresponding weights to compute the weighted sum of the function’s values at these nodes. Gaussian quadrature is named after the German mathematician Carl Friedrich Gauss, who contributed significantly to its development.

Gaussian quadrature provides more accurate results than other numerical integration methods, such as the trapezoidal rule or Simpson’s rule, especially for smooth functions. There are various types of Gaussian quadrature, including Legendre, Chebyshev, and Hermite quadrature, each with its own specific set of nodes and weights.