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MathGroup Archive 1989

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Orthogonal Polynomials

  • To: mathgroup
  • Subject: Orthogonal Polynomials
  • From: CLARK at ENH.NBS.GOV
  • Date: Wed, 22 Mar 89 14:37:22 CST

Regarding your response to an apparent bug in Tschebischeff (that's
the way I like it!) polynomial evaluation:

I discovered problems with several of the orthogonal polynomial
packages in M'ica Beta Release 0.1 f31 of 6/1/88 (enhanced vers.) on
a Mac II with the System and Finder current at the time (early
June 1988).  These were reported to WRI in the beta tester notebook
format, sent on a floppy.  I regret that I do not seem to have
retained a copy of the corespondence, nor have I tried to reproduce
the problems in version 1.1.  The problems became manifest in the
evaluation of standard recurrence formulae, in which sums of polynomials
of different orders must vanish. 0.1 f31 did OK when evaluating
these numerically, but would screw up at some values of the 
argument, such as 1/2, where it did its arithmetic in the clever
way.  I seem to recall that the Hermite, Jacobi, and Laguerre
polynomials exhibited this difficulty.

Regards,

Charles Clark 
CLARK at ENH.NBS.GOV





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