Re: Problem fitting a curve
From: tadchem (thomas.davidson_at_dla.mil)
Date: 03/03/05
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Date: 3 Mar 2005 06:43:28 -0800
proton wrote:
> I have to fit the following points using the given equation:
>
> points x(n): 0.39, 0.72, 1.00, 1.52, 2.8, 5.2, 9.54, 19.2, 30.1
>
> equation: a/x^2 + b/x + c log(x) = n*K, where n is an integer
>
>
> I have to find the best approximate values for the constants a, b, c,
> K.
>
> The problem is that the values of n are ANY integer, so instead of
> being n= 0, 1, 2, ... it could be n=-19, -18, -17, ...
>
> I need help to: 1. find the best fit for this equation and these
values
> (at least for a simple case, such as n= 0, 1, 2...) and 2. see if
there
> is a general way of tackling this kind of problem, when the sequence
> for n does not have any constraints.
>
> Any help will be very much appreciated.
To get started we must irst understand the problem.
Your given data:
"points x(n): 0.39, 0.72, 1.00, 1.52, 2.8, 5.2, 9.54, 19.2, 30.1"
only makes sense for curve fitting if the following table is used:
n | x(n)
---------
1 | 0.39
2 | 0.72
3 | 1.00
4 | 1.52
5 | 2.8
6 | 5.2
7 | 9.54
8 | 19.2
9 | 30.1
After all, it is a *curve-fitting* problem, and curves must be at least
two-dimensional, so it only makes sense if our points require at least
two coordinates to specify.
Plot x(n) versus n and you will see a curve. A semilog plot is
recommended.
Now you have 9 data points and 4 parameters, giving 5 degrees of
freedom for minimizing whatever criterion you are using to measure
deviation from "best" fit.
If this doesn't at least get you started, let us know.
Tom Davidson
Richmond, VA
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