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Minimax Approximation

• To: mathgroup at smc.vnet.net
• Subject: [mg60738] Minimax Approximation
• From: dh <dh at metrohm.ch>
• Date: Mon, 26 Sep 2005 04:05:42 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,
in numerical math, a common job is to fit some function with parameters 
"as well as possible" to either a given function or to a set of data 
points. "As well as possible" is mostly chosen to  mean "least square", 
that is the sum of squares of the error is minimized. However, there are 
cases wher one would like to minimize the largest error. This 
approximation scheme is called Minimax or L-infinity approximation. 
Unfortunately, Mathematica offers only a very restricted version for 
Minimax, that only works for rational function that are not zero.
Well, does anybody known a Mathematica implementation of a more useful general 
Minimax routine?
Daniel