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Datum: Mon, 17 Dec 2007 15:31:03 +0900
Von: Phil R. [email protected]
An: [email protected]
Betreff: Re: Curve fitting to data
fitting 21 data points with 4 parameters.
it is of course preferable to have some idea about the underlying
relationship between data graphed, such as
y = ax^2 + bx + c,
and then fit that model (this can be done by solving a linear
(numbering data points as ((x_0,y_0),…(x_n,y_)) and
[…] indicating rows in the matrix or row vectors)),
as this is a linear equation in the parameters a,b,c .
You can do that with any software that solves linear or matrix
equations, i.e., rsruby or rb-gsl .
It is of course also true that one can basically draw arbitrary
curves to connect data points, if you don’t know that a model
like the above is “true”.
Now, one additional line of thought is pursued in the discipline
of “approximation theory” (see eg., Wikipedia, or for a deeper
Here, one starts with a points, as yours, and asks,
Given a distance measure between the data and the curve (“norm”) and a
set of admissible model curves (e.g., all continuous curves on an
which curves will minimize that norm ?
There are indeed some results available, such as Chebyshev or
Remez(Remes) approximation procedures.
This kind of procedure can be recommended when the functional
relationship of your data is rather complicated/not enormously
simple models, you know something about the general wiggliness of the
underlying curve (see the Jackson theorems in Powell’s book), and you
need to have information about what you would have measured at some
point you didn’t actually measure and the result should be not too far