Numerical integration
Gaussian quadrature (derivation)
The Gaussian quadrature method is an optimal numerical integration technique for integrands of the form (polynomial) × (specific weight function). It allows for the exact integration of integrands of the form (2N-1 degree polynomial) × (weight function) by referencing only N points, despite the restriction on the positions of the points used for integration. Due to its ability to produce highly accurate results with a small number of points, it is particularly effective in the field of scientific and technical computation. This article will explain the theory behind the derivation of the Gaussian quadrature method.
Gaussian quadrature (Numerical Calculation)
Numerical Calculation for Gaussian quadrature