Normalized 1D Simple Quadrature Scheme Problem f(e)da a f 2 Area under the curve Is approximated by a rectangle SMA-HPC(2002 MIT Numerical Quadrature 4
Normalized 1D Simple Quadrature Scheme Problem Improving the Accuracy (ak2(1) 1/3 Area under the curve Is approximated by two rectangles x SMA-HPC(2002 MIT Numerical Quadrature 5
Normalized 1D Simple Quadrature Scheme Problem General n-Point Formula 1/元 f(a)daec∑ Key questions about the method How fast do the errors decay with n? Are there better methods? SMA-HPC⊙2002MT Numerical Quadrature 6
Normalized 1D Simple Quadrature Scheme Problem Numerical Example sin()ac 80m 10 10 SMA-HPC(2002 MIT Numerical Quadrature 7
Normalized 1D General Quadrature Scheme Problem General 1D Form f(a)dae-∑ f(m2) 0 i=1 weight Evaluation Point Free to pick the evaluation points Free to pick the weights for each poin An n-point formula has 2n degrees of freedom! SMA-HPC(2002 MIT Numerical Quadrature 8