# quadrature

Quadrature is the computation of a univariate definite integral. It can refer to either numerical or analytic techniques; one must gather from context which is meant. The term refers to the geometric origin of integration in determining the area of a plane figure by approximating it with squares.

Cubature refers to higher-dimensional definite integral computation. Likewise, this term refers to the geometric operation of approximating the volume of a solid by means of cubes (and has since been extended to higher dimensions).

The terms “quadrature” and “cubature” are typically used in numerical analysis to denote the approximation of a definite integral, typically by a suitable weighted sum. Perhaps the simplest possibility is approximation by a sum of values at equidistant points, i.e. approximate $\int_{0}^{1}f(x)\,dx$ by $\sum_{k=0}^{n}f(k/n)/n$. More complicated approximations involve variable weights and evaluation of the function at points which may not be spaced equidistantly. Some such numerical quadrature methods are Simpson’s rule, the trapezoidal rule  , and Gaussian quadrature.

Title quadrature Quadrature 2013-03-22 12:07:35 2013-03-22 12:07:35 rspuzio (6075) rspuzio (6075) 13 rspuzio (6075) Definition msc 28-00 msc 65D32 msc 41A55 msc 26A42 cubature