Math 6610 • Analysis of Numerical Methods I

(Quadrature rules) Compute the weights \(\{A_0, A_1, B_0, B_1\}\) for a 4-point quadrature rule of the form \[ \int _0^1 f(x)\,dx \approx A_0 f(0) + A_1 f(1) + B_0 f'(0) + B_1 f'(1) \]

that is exact when \(f\) is any polynomial of degree 3 or less.