http://www.arsmathematica.net/archives/2008/09/12/gaussian-quadrature/ Dedicated to the mathematical arts. Thu, 08 Jan 2009 12:22:08 +0000 http://wordpress.org/?v=2.5.1 http://www.arsmathematica.net/archives/2008/09/12/gaussian-quadrature/#comment-62378 Dan Sun, 09 Nov 2008 06:50:55 +0000 http://www.arsmathematica.net/?p=706#comment-62378 I'd say that the existence of Gaussian quadrature isn't nearly as surprising as the unreasonable effectiveness of the Trapezium rule applied to a periodic function. This is not to say that the former isn't surprising, it's just that the latter demonstrates that sometimes the simplest methods are the best. One of my favourite things about Gaussian quadrature is its link to the convergence of the Conjugate Gradient method (via that Lanczos algorithm). I’d say that the existence of Gaussian quadrature isn’t nearly as surprising as the unreasonable effectiveness of the Trapezium rule applied to a periodic function. This is not to say that the former isn’t surprising, it’s just that the latter demonstrates that sometimes the simplest methods are the best. One of my favourite things about Gaussian quadrature is its link to the convergence of the Conjugate Gradient method (via that Lanczos algorithm).

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