[Scipy-tickets] [SciPy] #1466: More accurate roots/weights for Gauss-Hermite quadrature
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Mon Jul 4 15:03:31 CDT 2011
#1466: More accurate roots/weights for Gauss-Hermite quadrature
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Reporter: Bogdan | Owner: pv
Type: enhancement | Status: new
Priority: normal | Milestone: Unscheduled
Component: scipy.special | Version: devel
Keywords: |
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Comment(by charris):
I've played with this a bit more.
1) Numpy's Hermite zero finder dies up around deg 70. I need to symmetrize
the companion matrix
2) Scipy needs to use eigh instead of eig, but this doesn't help much. The
eigenvectors are also off.
3) Using zeros from Scipy, improving them with Newton, and using the w =
a/(H_{n}'(r)*H_{n-1}), where a is chosen so that the w sum up to sqrt(pi),
works well.
Note that the routine form NR also uses Newton. I've attached a plot with
the weights from the three (eig, eigh, improved), where the improved
behavior for degree 100 is easy to see.
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Ticket URL: <http://projects.scipy.org/scipy/ticket/1466#comment:3>
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