Is Gauss Quadrature Better than Clenshaw–Curtis?
Is Gauss Quadrature Better than Clenshaw–Curtis?
We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O'Hara and Smith …