# 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 ${\int}_{0}^{1}f(x)\mathit{d}x$ 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 |
---|---|

Canonical name | Quadrature |

Date of creation | 2013-03-22 12:07:35 |

Last modified on | 2013-03-22 12:07:35 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 13 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 28-00 |

Classification | msc 65D32 |

Classification | msc 41A55 |

Classification | msc 26A42 |

Defines | cubature |