formulas for approximating definite integrals by means of the values of the integrand at a finite number of points. The most common quadrature formulas have the form

where x1x2, …, xn are the nodes of the quadrature formula, A1, A2 . . . ,An are its coefficients, and Rn is the remainder term. For example,

where a ≤ ξ ≤ b (trapezoidal rule). Sometimes for mulas for mechanical, or numerical, quadrature are also called quadrature formulas.

### REFERENCE

Krylov, V. I. Priblizhennoe vychislenie integralov, 2nd ed. Moscow, 1967.
References in periodicals archive ?
In sparse grids, quadrature formulas of high order for some dimensions are combined with quadrature formulas of lower order for the remaining dimensions in a way that the interpolation error is equivalent to that of full tensor products.
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Quadrature formulas based on rational interpolation.
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The quadrature formulas are interpolatory and therefore the degree of exactness is at least n.

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