🚀 go-pugleaf

In article <1989Sep28.161516.10353@rpi.edu> wrf@mab.ecse.rpi.edu (Wm Randolph Franklin) writes:

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>You can   work out  how many  Taylor  terms  it would  take  to get that
>accuracy.  Editorial: Taylor series are for wimps.

I'm under the impression that in any given range which doesn't have
singularity points, Chebyshev polynomials (of the first kind) can be
used to "telescope" Taylor series of degree N down to degree N-1
while retaining the same maximum error (but this error may pop up in
places where it wasn't present in the original--kinda like squeezing
a balloon).  The difference between N and N-1 is only ONE term
(although for some common trig functions which have only even- or odd-
powered terms, it may LOOK like two?); which seems rather "wimpy" to me.

I can see that if I'm going to calculate a particular series a jillion
times, one less calculation would be nice, but I don't see that as
being particularly significant otherwise.  Do other Chebyshev
polynomials provide even better telescoping?

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--Myron.
--
Myron A. Calhoun, PhD EE, W0PBV, (913) 532-6350 (work), 539-4448 (home).
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