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Numerical Quadrature

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2044)

Abstract

In this chapter we discuss numerical approximation of the integral

$$\begin{array}{rcl} I(f) ={ \int \nolimits \nolimits }_{{\mathbb{S}}^{2}}f(\eta )\,d{S}^{2}(\eta ).& &\end{array}$$
(5.1)

The integrand fcan be well-behaved or singular, although our initial development assumes fis continuous and, usually, several times continuously differentiable. Such integrals occur in a wide variety of physical applications; and the calculation of the coefficients in a Laplace series expansion of a given function (see (4.55)) requires evaluating such integrals.

Keywords

  • Gauss Product Formula
  • Hyperinterpolation
  • Centroid Rule
  • Minimax Error
  • Centroid Method

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 5.1
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Fig. 5.4

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© 2012 Springer-Verlag Berlin Heidelberg

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Atkinson, K., Han, W. (2012). Numerical Quadrature. In: Spherical Harmonics and Approximations on the Unit Sphere: An Introduction. Lecture Notes in Mathematics(), vol 2044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25983-8_5

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