Discussion:  All in Calculus 
Topic:  Tool: Polynomial Fitting 
Related Item:  http://mathforum.org/mathtools/tool/2141/ 
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Subject:  RE: Tool: Polynomial Fitting 
Author:  Craig 
Date:  Jul 23 2004 
is true that through any n points (with different xvalues) a polynomial
spline may be constructed; it's a fairly straightforward (though computationally
onerous) process using linear algebra only. However, to "fit" a polynomial
curve of a fixed degree through a set number of points involves decision
makingshould the curve go closer to point A or to point B, or is it
important that it pass through both? There is not a "standard" answer to the
problem, so there is not a unique deterministic way to find the "best" fit (even
for fitting a line to more than two points opens discussionleast squares
versus minimum absolute error, or even medianmedian process). It may be that
the particular algorithm used requires a couple of derivatives (fitting, say,
location and slope), so the two extra points required give nonsingular
solutions.
 
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