Gaussian quadrature (intro)
General · Mathematics
Study notes
Q: Use 2-point Gauss-Legendre to approximate ∫₋₁¹ x² dx. Compare exact. Nodes: ±1/√3 ≈ ±0.5774. Weights: 1, 1. G = f(-0.5774)+f(0.5774) = 0.3333+0.3333 = 0.6667. Exact: [x³/3]₋₁¹ = 2/3 ≈ 0.6667. EXACT! 2 points exact for degree 3 (vs Simpson needs 3)! (Optimal node placement!)