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From: "Per Sundqvist" <sunkan@fy.chalmers.se>
Newsgroups: comp.soft-sys.matlab
Subject: Re: the mathematic relationship between two series of data
Date: Sun, 13 Jul 2008 18:05:03 +0000 (UTC)
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"John D'Errico" <woodchips@rochester.rr.com> wrote in
message <g5d55p$a3$1@fred.mathworks.com>...
> "Hong Zhang" <oceanzhhd@gmail.com> wrote in message 
> <g5d0sv$2un$1@fred.mathworks.com>...
> > Hi,John,
> > 
> > "it sounds as if you do not have any mechanistic or 
> > physical model for yourdata", That's to the point. 
> > Actually, in my former dataset, A is the interval of a 
> > series of measurment value and B is corresponding 
> > cumulative probability. As there is no reference about the 
> > distribution rule of such measurment, at first i think it 
> > would be power-law which may be accord with the real life 
> > condition.
> 
> If it should be some sort of a power law,
> think about the form. You might consider
> reading through my nonlinear shapes
> submission:
> 
>
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?
> objectId=10864&objectType=FILE
> 
> 
> > I had no clear idea until now. Why it appears to be a 
> > piecewise quadratic? why it has a small break? In fact, A 
> > is the result of another matalb programming which is point 
> > to an adjacency matrix.
> > 
> > Your suggestions do give me some hints and clues. I need to 
> > think carefully about the mechanism of the independent 
> > variable and its real life meaning.
> 
> Exactly. It is this introspection that is very
> important when you do modeling. It helps
> you to learn about your process, and perhaps
> discover things that you know about the
> system that you might not have seen
> otherwise.
> 
>  
> > BTW, Is estimatenoise to used to evaluate or improve the 
> > curvefitting precision? It is obiviously important to be 
> > considered.
> 
> Estimatenoise might help you if you are
> using a smoothing spline to approximate
> the relationship, since they can use that
> information.
> 
> 
> > But for me, this curvefitting process is 
> > something like data mining. i concerns what relationship 
> > the dataset emerge and why it appears like that.
> 
> Curvefitting can be a voyage of discovery,
> helping you to learn about the process you
> will fit. Or it can be as simple as a brute
> force interpolation, or polynomial curve fit.
> You may receive returns that are directly
> related to the effort you expend in the
> modeling process.
> 
> John

It looks like you should have y(1)=30 and y(0)=100 and
y'(0)=0. I think you could use the mechanical fourth order
differential equation in 1D to model this, using appropriate
BC and stiffnes parameters. Then fit your data to this
analytic formula, its related to linear combinations of
sinh, cosh, sin and cos in some way.