Re: algorithm used in the non-linear solver

[Frederic Parrenin <parrenin gmail com>]

Hi Morten,

If you are doing Newton iterations near the root, it seems easy to
export the matrix of the second derivatives somewhere in the workbook.
It would be very useful to evaluate how 'localized' is the root. (or
in inverse problems terms, what are the confidence intervals of the
most likely scenario)

Best regards,

Frédéric



2012/7/9 Morten Welinder <mortenw gnome org>:
> It's mostly based on this:
>
> Rosenbrock, H. H. (1960), "An automatic method for finding the
> greatest or least value of a function", The Computer Journal 3:
> 175–184, DOI:10.1093/comjnl/3.3.175, ISSN 0010-4620, MR0136042
>
> (Fifty-year old cutting-edge tech, eh?)
>
> It's not pure, though.  I found it beneficial to occasionally take a
> few tentative Newton iterations based on numerical derivation.  This
> is useful because Newton iteration is very, very fast when
> sufficiently close to the root.
>
> So there.  Nothing really fancy.
>
> Note, that this is all in a plugin ("nlsolve") so if anyone feels like
> writing another algorithm up for a solver, it's not that much work.
> This one is ~800 lines.
>
> Morten



-- 
http://parrenin.frederic.free.fr/