[Scipy-tickets] [SciPy] #1466: More accurate roots/weights for Gauss-Hermite quadrature

SciPy Trac scipy-tickets@scipy....
Tue Jun 28 01:37:51 CDT 2011


#1466: More accurate roots/weights for Gauss-Hermite quadrature
---------------------------+------------------------------------------------
 Reporter:  Bogdan         |       Owner:  pv         
     Type:  enhancement    |      Status:  new        
 Priority:  normal         |   Milestone:  Unscheduled
Component:  scipy.special  |     Version:  devel      
 Keywords:                 |  
---------------------------+------------------------------------------------

Comment(by Bogdan):

 Yes, this trick certainly does improve the accuracy. Although recursive
 algorithm is still slightly better; comparing it with this function:
 {{{
 def h_roots_numpy(n):
         p = H([0]*n + [1])
         r = p.roots()
         r1 = r - p(r)/(p.deriv()(r))
         return r1, (2 ** (n-1)) * factorial(n) * numpy.sqrt(numpy.pi) /
 (p.deriv()(r1) ** 2) * 4.0
 }}}
 for N=77, M=70 I get
 {{{
 Numpy roots: 0.823443522596
 Recursive roots: 1.0
 }}}
 And with increasing N h_roots_numpy() just goes haywire.

-- 
Ticket URL: <http://projects.scipy.org/scipy/ticket/1466#comment:2>
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