Re: Problem with the Gaussian Quadrature package

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: Problem with the Gaussian Quadrature package*From*: keiper*Date*: Fri, 27 Aug 93 18:19:58 CDT

> There also seems to be a problem with large n. ... > Where does 0000. come from? When numbers are so imprecise that not even the first digit is known they are printed as an inexact zero in a way that indicates the amount of imprecision. Thus "0000." indicates that the imprecision is about 10^4, while ".000" indicates that the imprecision is about 10^-3. There are ways to calculate the Gaussian coefficients without a great deal of precision loss, but it is not an easy problem. (The internal code for NIntegrate[ ] does this, but it is a fair bit of code.) The Gaussian Quadrature package is intended as much for instructional purposes as anything else so I decided to implement it in a way that was most easy to understand even though it is not the most numerically stable approach. The idea is that the user can always increase the precision to get the required precision in the results. Jerry B. Keiper keiper at wri.com Wolfram Research, Inc.