Problem with the Gaussian Quadrature package

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Problem with the Gaussian Quadrature package*From*: prange at sdr.slb.com (Michael Prange)*Date*: 24 Aug 1993 10:09:09 -0400 (EDT)

I found a problem with the GaussianQuadrature package distributed with mma 2.2 on a sparc10. Here is the version info: (* :Package Version: Mathematica 2.0 *) (* :History: Original version by Jerry B. Keiper, May 1990. Revised by Jerry B. Keiper, December 1990. *) When I evaluate GaussianQuadratureWeights[1, 0, 1, 16] I get {{0, 2.}}. According to Abramowitz and Stegun table 25.8 (p. 921) the answer should be {{.5, 1}}. The problem with the code seems to be with the line If[ n == 1, Return[N[{{0, 2}}, prec]]]; My guess is that this line should be If[ n == 1, Return[N[{{(b+a)/2, b-a}}, prec]]]; There also seems to be a problem with large n. Linearsolve complained of a loss of precision, so I boosted the precision from 16 to 32. The resulting quadrature weights are In[23]:= Map[Last,GaussianQuadratureWeights[40, 0, 1, 32]] Out[23]= {0, 0.013, -0.01, 0.00, 0.0, 0.0, 0., 00., 00., 000., 000., 000., > 000., 000., 000., 000., 000., 00., 0., 0000., 0000., 0., 00., 000., > 000., 000., 000., 000., 000., 000., 000., 00., 00., 0., 0.0, 0.0, 0.00, > -0.01, 0.013, 0} Where does 0000. come from? Michael prange at sdr.slb.com