Re: Problem fitting a curve

From: maison.mousse (maison.mousse_at_wanadoo.fr)
Date: 03/03/05 

Date: Thu, 3 Mar 2005 17:18:10 +0100

tadchem a écrit dans le message
<1109861008.762461.316630@g14g2000cwa.googlegroups.com>...
>
>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
>

You are correct! If you use the data as above and plot
n on the x axis and x(n) on the log y axis the result is a fairly straight
line.

You might want to look at this site.
http://curvefit.com/

JOL

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