Re: fixed points piecewise-linear fitting

[Juan Pablo Carbajal]

On Sat, Mar 17, 2012 at 10:32 PM, Ben Abbott <address@hidden> wrote:
> On Mar 17, 2012, at 2:22 PM, Sergei Steshenko wrote:
>
>> ----- Original Message -----
>>> From: Ben Abbott <address@hidden>
>>> To: Sergei Steshenko <address@hidden>
>>> Cc: help-octave Octave <address@hidden>
>>> Sent: Saturday, March 17, 2012 6:39 PM
>>> Subject: Re: fixed points piecewise-linear fitting
>>>
>> [snip]
>>>
>>> I mean that linear least squares can be used to solve this problem.
>>>
>>> Ben
>>
>> I am not sure - because of _piecewise_-linear requirement. I am not even 
>> sure only one solution exists.
>>
>> Regards,
>>   Sergei.
>
> After taking a closer look, I agree. A linear least squares approach will not 
> work.
>
> Since I've been wanting a function that does this sort of thing, I put coded 
> a simple solution that results a piece-wise polynomial.
>
> It includes the tex-info help as well as a demo. I used fsolve() to determine 
> the interpolating values. So, it is not speedy or efficient.
>
> Ben
>
>
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>

If you accept the min square idea (which makes a lot of sense). You
are solving what any FEM in 1D would solve when using linear elements
center in your Yf. You are projection your (X,Y) function into the
tent space. I will search my teaching code. I have a function to do it
somewhere there. In the meanwhile somebody could update us about FEM
1D in Octave?
Maybe Carlo knows about this.

-- 
M. Sc. Juan Pablo Carbajal
-----
PhD Student
University of Zürich
http://ailab.ifi.uzh.ch/carbajal/