Chapter 5 Numerical Quadrature and Differentiation

Estimating \(\int_{a}^{b}f(x)dx\) using sums of the form \(\sum_{i=0}^{n}w_{i}f(x_{i})\) is known as the quadrature problem. Here \(w_{i}\) are called weights, and \(x_{i}\) are called nodes. The objective is to determine the nodes and weights to minimize error.