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