Gaussian Quadrature Examples

Numerical Analysis · Axiom Academy

Apply 2-point Gauss-Legendre quadrature to approximate an integral You've successfully applied Gaussian quadrature! Change of variables: Always transform [a, b] to [-1, 1] using x = (b-a)t/2 + (a+b)/2 Node locations: Gauss-Legendre nodes are roots of Legendre polynomials— not evenly spaced! Efficiency: n-point Gaussian quadrature is exact for polynomials up to degree 2n-1 Accuracy: Even with just 2 points, we achieved very high accuracy (error ≈ 0.005) Gaussian quadrature is optimal for smooth functions when you can choose evaluation points freely!

This is the written version of the interactive lesson above. See the full Numerical Analysis course.