Quadrature

Concept

basically

$${\int }_a^{b}f(x)=\sum _i^n{w}_i(x)f(x_i)$$

stability upper bound

$$|\Delta Q|\le ||w|{|}_1\max |\Delta f_i|$$

Implementation

Newton-Cotes Quadrature use uniformly spaced nodes, Gaussian Quadrature use optimal picked nodes