From Simpson to Kronrod: An Elementary Approach to Quadrature Formulae

摘要

Quadrature formulae, or rules, are used in the approximate evaluation of integrals. This is an elegant and extremely useful branch of numerical analysis; even the most powerful methods are actually based on very simple mathematics. In this article, we will examine the ideas behind a number of quadrature formulae. Typically, the integrand is a complicated object, and the aim of the game is to obtain the most accurate estimate, with the minimum possible computation.