[Maxima] references to methods, algorithms behind lsquares

Robert Dodier robert.dodier at gmail.com
Wed Feb 1 00:54:50 CST 2012


On 1/31/12, gwpublic at wp.pl <gwpublic at wp.pl> wrote:

> For lsquares there are no such nice references:
> http://maxima.sourceforge.net/docs/manual/en/maxima_65.html#SEC304
>
> I'd like to cite in my thesis to works behind lsquares, as I use it
> (to be more specific: lsquares_estimates , lsquares_mse ).

Well, lsquares_estimates tries to find an exact minimum of the
mean square error, via the Maxima function "solve".
If solve cannot find a solution, then lsquares_estimates tries
to find an approximate minimum, via the function "lbfgs",
which is an implementation of the LBFGS algorithm, which
is a limited-memory BFGS (quasi-Newton) algorithm.
"?? lbfgs" finds some info in the reference manual.

> One more issue : What's are best terms for lsquares ?
>
> I'd like to call it somehow, I am curious about recommendations for
> "terms" describing lqaures, like :
> Optimization Search Routine ?
> Optimisation in Symbolic Mathematics ?
> Data fitting of parametrised symbolic mathematics ?

I think it's what's commonly called "estimation" or
more specifically "least squares estimation".

best,

Robert Dodier


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