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