Re: [Help-glpk] Applying a threshold to the solution using GMPL?

[Michael Hennebry]

On Mon, 11 Nov 2013, Reginald Beardsley wrote:

> Marc's suggestion fits very nicely with what I'm trying to do at the moment.
>
> I sometimes get terms which constitute much less than 1% of the total result.  
> Those are what I want to drop.  Doing so requires recalculating the other terms 
> to minimize the error.

Of course you will want to recalculate.
If you have fifty one-percenters,
you will want to recalculate your solution.
If you have a thousand one-percenters,
you will want to recalculate your threshold.
Marc's works if you already know your threshold.

> I may want to do something fancier eventually, but right now I'm still trying 
> to develop an appropriate mathematical model for the physics.
>
> That said, there's another problem for which what is suggested here looks very 
> attractive.  I've attempted to solve that problem several times over the course of 
> 20+ years without ever finding a satisfactory solution.  It involves finding the 
> derivative of a series irregularly sampled in x with truncation errors in both x 
> & y.  When the data are finely sampled in x the truncation to 3-4 digits in y 
> leads to wild swings in the derivative.  To date the only solution has been 
> smoothing based on ersatz heuristics.  Good enough, but not aesthetically 
> satisfying.

You might want to consider doing something related to splines.
The values at the knots would have ranges rather than fixed values.
In the case of a cubic spline, you might want to minimize the
sum of the squares of the third derivitives or something.

--
Michael   address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword."  --  Lily