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MathGroup Archive 2000

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Problem with the GaussianQuadratureWeights[n, a, b]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26431] Problem with the GaussianQuadratureWeights[n, a, b]
  • From: Cheng Liu <cliu at lanl.gov>
  • Date: Wed, 20 Dec 2000 00:21:50 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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.
?::indet :
     Indeterminate expression - 1672.96 + ComplexInfinity +
       ComplexInfinity + \[LeftSkeleton]6\[RightSkeleton] + ComplexInfinity +
       ComplexInfinity encountered.
Out[43]=
{{0.000800191, Indeterminate}, {0.00421136, Indeterminate}, {0.0103287,
     Indeterminate}, {0.0191203, Indeterminate}, {0.0305382,
     Indeterminate}, {0.0445201, Indeterminate}, {0.0609897,
     Indeterminate}, {0.079857, Indeterminate}, {0.101019,
     Indeterminate}, {0.12436, Indeterminate}, {0.149753,
     Indeterminate}, {0.177058, Indeterminate}, {0.206128,
     Indeterminate}, {0.236802, Indeterminate}, {0.268914,
     Indeterminate}, {0.302288, Indeterminate}, {0.336742,
     Indeterminate}, {0.372087, Indeterminate}, {0.408132,
     Indeterminate}, {0.444677, Indeterminate}, {0.481526,
     Indeterminate}, {0.518474, Indeterminate}, {0.555323,
     Indeterminate}, {0.591868, Indeterminate}, {0.627913,
     Indeterminate}, {0.663258, Indeterminate}, {0.697712,
     Indeterminate}, {0.731086, Indeterminate}, {0.763198,
     Indeterminate}, {0.793872, Indeterminate}, {0.822942,
     Indeterminate}, {0.850247, Indeterminate}, {0.87564,
     Indeterminate}, {0.898981, Indeterminate}, {0.920143,
     Indeterminate}, {0.93901, Indeterminate}, {0.95548,
     Indeterminate}, {0.969462, Indeterminate}, {0.98088,
     Indeterminate}, {0.989671, Indeterminate}, {0.995789,
     Indeterminate}, {0.9992, Indeterminate}}

When n > 50, the above behavior disappears.  Of course, I didn't check
cases when n is really big (it's also not necessary in view of ordinary
numerical computation).  The version of Mathematica I am using is
"4.0 for Power Macintosh (July 26, 1999)".  Any explanations?

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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