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Subject: Re: Piecewiese linear approximation function with a minimal largest error dev.
Date: Wed, 2 Jan 2013 09:06:08 +0000 (UTC)
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <kc0oak$dm$1@newscl01ah.mathworks.com>...
> As I told earlier, if the knot are fixed (regardless they are is equidistant or not) , this problem is a first-degree spline-approximation (piece-wise linear) of l_infinity norm, and can be formulated as linear programming.
> 
> Bruno
- - - - - - - - -
  Bruno, we seem to be looking at Deyan's problem from two different aspects.  You are saying that given an L_infinity norm the problem can be solved as a linear programming problem and you may well be right.  I have been saying that its primary difficulty lies in calculating this L_infinity norm since it involves not just the differences at the segment endpoints which would involve a finite number of variables but the differences occurring between these endpoints where an infinite continuum of points are involved.  That is why I spoke of the inverse of derivatives or numerous intermediate points.  Please correct me if I am mistaken.

Roger Stafford