Path: news.mathworks.com!not-for-mail
From: "Hailey Yang" <haileyyang@hotmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Is it possible to optimize a spline function?
Date: Mon, 6 Oct 2008 21:17:03 +0000 (UTC)
Organization: M.I.T.
Lines: 38
Message-ID: <gcdv8f$svq$1@fred.mathworks.com>
References: <gbug8e$2ae$1@fred.mathworks.com> <gbvk24$a2m$1@fred.mathworks.com> <gc0i54$5c6$1@fred.mathworks.com> <gc64fd$i3k$1@fred.mathworks.com> <gc67f2$pnu$1@fred.mathworks.com>
Reply-To: "Hailey Yang" <haileyyang@hotmail.com>
NNTP-Posting-Host: webapp-05-blr.mathworks.com
Content-Type: text/plain; charset="ISO-8859-1"
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1223327823 29690 172.30.248.35 (6 Oct 2008 21:17:03 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Mon, 6 Oct 2008 21:17:03 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1433718
Xref: news.mathworks.com comp.soft-sys.matlab:493910


Thanks again for your reply. As for the multivariate spline approximation, I looked into the help file for spline toolbox by searching "multivariate spline", but didn't find much helpful information on what command I am supposed to do it. 

I tried to use csapi, but it doesn't work once my variables x becomes a matrix, which seems suggesting that it only works for univariate approximation.

In the help file, the only relevant command to do multivariate spline is "stform", but I don't quite understand how this works even after I read the help file. Also it is said in the help file that: "At present, the toolbox works with just one kind of stform, namely a bivariate thin-plate spline and its first partial derivatives. ". Does this mean that it won't work if my function is determined by more than two variables?  

Will there be other functions/commands that can do multivariate spline approximation that I missed? 

Hailey  

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <gc67f2$pnu$1@fred.mathworks.com>...
> "Hailey Yang" <haileyyang@hotmail.com> wrote in message <gc64fd$i3k$1@fred.mathworks.com>...
> > Thank you for your reply. My understanding for the spline approximation, which might be wrong, is that the whole region, if necessary, is seperated into different regions and each region is represented by a polynomial function.
> 
> Yes. A spline is a piecewise polynomial model,
> that approximates your function from your
> data points. The knots or break points specify
> the locations where the pieces are tied together.
> 
> 
> > In that case, will there be any problem with optimizing each region and then comparing the optimums to get the global optimum?
> 
> Why should there be a problem?
> 
> 
> > I guess there is a question sort of embeded in this question, which is whether the polynomial function is always convex at the positive variable region (since variables are positive in my problem). 
> 
> There is no such constraint on a spline such
> that it satisfies any convexity constraints, at
> least unless you have constructed the spline
> such that this is true.
> 
>  
> > Another seperate question is that: is it possible to do so for multivariate spline approximation? 
> 
> Yes.
> 
> John