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MathGroup Archive 1996

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desperately seeking better minimax approximation package

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4158] desperately seeking better minimax approximation package
  • From: John Bunda <bunda at centtech.com>
  • Date: Sat, 8 Jun 1996 13:24:13 -0400
  • Organization: Centaur Technology, Inc.
  • Sender: owner-wri-mathgroup at wolfram.com

The one that comes with Mathematica is not general enough
for my application.  Does anyone know of other packages
(preferably, not necessarily Mathematica) for doing this?

Specifically, what we'd like to be able to do is approximate
a continuous function with a even or odd polynomial, such that
the maximum error is minimized. For example, sin(x) could be
approximated as:
    p(x) = c1x + c3*x^3 + c5*x^5 + ...
where c1, c3, and c5 are chosen to minimize the maximum error 
between p(x) and sin(x).  The trouble with the minimax package
that comes with Mathematica is it requires me to have terms
with strictly sequential powers - I can't skip the x^2 and x^4
terms like in the above series.

Is there anything more general available?

Thanks in advance.

-John

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