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 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
I believe the "n-2" versus "n-1" issue is a result of the process used.  It
is true that through any n points (with different x-values) 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
making--should 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 discussion--least squares
versus minimum absolute error, or even median-median 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 non-singular
solutions.