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Re: Re: Problem with the GaussianQuadratureWeights[n, a, b]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26462] Re: [mg26444] Re: Problem with the GaussianQuadratureWeights[n, a, b]
  • From: Cheng Liu <cliu at lanl.gov>
  • Date: Thu, 21 Dec 2000 22:46:46 -0500 (EST)
  • References: <91pjn3$5vp@smc.vnet.net> <200012210651.BAA08643@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Thank you Jens,

	By setting the precision higher than the default (16) solve the
problem described in my previous post.  But another problem appears,

In[9]:=
GaussianQuadratureWeights[7, 0, 1, 20]
Out[9]=
\!\({{0.0254460438286207377369051579760743056`24.7499,
       0.08184679159616065512531181311972918224`22.9004}, \
{0.1292344072003027800680676133596057328`25.5629,
       0.176800361948499354889282418503202`22.9376}, \
{0.2970774243113014165466967939615192127788252`26.1861,
       0.241352841905111882955195047583155`22.9492}, {1\/2,
       9.1004562140604214415812457652156224`23.0189*^-9}, \
{0.70292257568869858345330320603848078722`26.5602,
       0.241352841905111882955195047583156`22.9064}, \
{0.8707655927996972199319323866403942672`26.3914,
       0.176800361948499354889282418500441`22.3581}, \
{0.9745539561713792622630948420239256944`26.3331,
       0.081846791596160655125311813120987`22.4951}}\)

Note the point at x=1/2, w is almost zero, which should be around 0.2.

Another observation is that GaussianQuadratureWeights[7, 0, 1, 20] and
GaussianQuadratureWeights[7, 0, 1] give different answers to the weight
w.  Any help would be appreciated.  Thanks.

Cheng



>Hi,
>
>setting the precision will help and
>
>GaussianQuadratureWeights[42, 0, 1, 32]
>
>work fine.
>
>Cheng Liu wrote:
>>
>>  Hi,
>>
>>          I accidently run into this strange behavior.  I am using the
>>  package NumericalMath`GaussianQuadrature` and the function
>>  GaussianQuadratureWeights[n, a, b] to obtain the abscissas and weights
>>  for the n-point Gaussian quadrature formula on the interval (a, b).
>>  The specific interval in my problem is (0, 1),  I noticed that
>>  when 40 <= n <= 50, if n is odd, the function gives correct answer,
>>  but when n is even, the function gives the following error message:
>>
>>  In[43]:=
>>  GaussianQuadratureWeights[42, 0, 1]
>>  \!\(Power::"infy" \(\(:\)\(\ \)\)
>>       "Infinite expression \!\(1\/0.`\) encountered."\)
>>  \!\(Power::"infy" \(\(:\)\(\ \)\)
>>       "Infinite expression \!\(1\/0.`\) encountered."\)
>>  \!\(Power::"infy" \(\(:\)\(\ \)\)
>>       "Infinite expression \!\(1\/0.`\) encountered."\)
>>  General::stop :
>>       Further output of Power::infy will be suppressed during this 
>>calculation.
>>  f::indet :
>>       Indeterminate expression - 1672.96 + ComplexInfinity +
>>         ComplexInfinity + \[LeftSkeleton]6\[RightSkeleton] + 
>>ComplexInfinity +
>>         ComplexInfinity encountered.
>SNIPP SNAPP
>>  Thanks.
>>
>>  Cheng
>>  --

-- 
====================================================
Cheng Liu, Ph.D.
MST-8, Structure/Property Relations
Materials Science and Technology Division
Los Alamos National Laboratory
Los Alamos, New Mexico 87545

Phone: 505-665-6892 (office), 505-667-9950 (lab)
Fax:   505-667-8021
email: cliu at lanl.gov
====================================================


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