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MathGroup Archive 2007

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NIntegrate - Gaussian quadrature more exact than thought

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73833] NIntegrate - Gaussian quadrature more exact than thought
  • From: "janos" <janostothmeister at gmail.com>
  • Date: Thu, 1 Mar 2007 06:23:13 -0500 (EST)

NIntegrate[x^4, {x, 0, 1}, Method->GaussKronrod, GaussPoints->2]

gives 0.2, the exact result, although the Gauss quadrature should be
inexact on a polynomial of degree 2n+2 where n is the number of
GaussPoints. More exactly, we expected the same results as here:

<< NumericalMath`GaussianQuadrature`
gw = GaussianQuadratureWeights[2, 0, 1]
f[{x_, y_}] := x^4 y
Total[f /@ gw]
0.194444

This is inexact, OK.

Why is NIntegrate so good?
Something I may have missed.

Thank you for your help.

Janos



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