1990•Journal of Engineering MechanicsRequires access

Numerical Differentiation Using Gaussian Quadrature

B. L. Ly

Abstract

A numerical method is derived for finding the slope of a function from its tabulated values. This method requires that the interpolation function directly approximate the slope in the mean-square sense. In this way, a formal differentiation of the interpolation function is avoided. As a result of the mode of approximation, it turns out that numerical integration, not numerical differentiation, is what is needed for finding the slope. An advantage of this feature is the possibility of using the Gaussian quadrature to derive a formula for nonequidistant sampling points.

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Available abstract

Key concepts: Numerical integration, Gauss–Kronrod quadrature formula, Tanh-sinh quadrature, Gaussian quadrature, Numerical differentiation, Mathematics, Clenshaw–Curtis quadrature, Interpolation (computer graphics)