NumericalDifferentialEquationAnalysis`
NumericalDifferentialEquationAnalysis`
GaussianQuadratureWeights
GaussianQuadratureWeights[n,a,b]
gives a list of the n pairs {xi,wi} of the elementary n-point Gaussian formula for quadrature on the interval a to b, where wi is the weight of the abscissa xi.
GaussianQuadratureWeights[n,a,b,prec]
attempts to give a result with prec digits of precision.
Details and Options
- To use GaussianQuadratureWeights, you first need to load the Numerical Differential Equation Analysis Package using Needs["NumericalDifferentialEquationAnalysis`"].
- Gaussian quadrature approximates the value of an integral as a linear combination of values of the integrand evaluated at optimal abscissas
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- The abscissas are optimal in the sense that the quadrature formula is exact for all polynomials up to degree 2n-1.