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
====================================================
- References:
- Re: Problem with the GaussianQuadratureWeights[n, a, b]
- From: Jens-Peer Kuska <kuska@informatik.uni-leipzig.de>
- Re: Problem with the GaussianQuadratureWeights[n, a, b]