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2014•Wiley StatsRef: Statistics Reference OnlineRequires access

Quadrature and Numerical Integration

M. Concepción Ausín

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Abstract

Abstract The objective in numerical integration is the approximation of a definite integral using numerical techniques. There is a large number of numerical integration methods in the literature and this article overviews some of the most common ones, namely, the Newton–Cotes formulas, including the trapezoidal and Simpson's rules, and the Gaussian quadrature. Different procedures are compared and illustrated with examples. Discussions about more advanced numerical integration procedures are also included.

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What this paper is about

Abstract The objective in numerical integration is the approximation of a definite integral using numerical techniques. There is a large number of numerical integration methods in the literature and this article overviews some of the most common ones, namely, the Newton–Cotes formulas, including the trapezoidal and Simpson's rules, and the Gaussian quadrature. Different procedures are compared and illustrated with examples. Discussions about more advanced numerical integration procedures are also included.

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Available abstract

Abstract The objective in numerical integration is the approximation of a definite integral using numerical techniques. There is a large number of numerical integration methods in the literature and this article overviews some of the most common ones, namely, the Newton–Cotes formulas, including the trapezoidal and Simpson's rules, and the Gaussian quadrature. Different procedures are compared and illustrated with examples. Discussions about more advanced numerical integration procedures are also included.

Key concepts: Numerical integration, Gaussian quadrature, Gauss–Kronrod quadrature formula, Quadrature (astronomy), Numerical analysis, Tanh-sinh quadrature, Clenshaw–Curtis quadrature, Applied mathematics

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