Re: [Maxima-discuss] derive halley's method for vector valued functions

[Robert D. <rob...@gm...>]

I've spent a pleasant day working on this problem and got some results
which seem to be consistent with the Cuyt & Rall paper
(http://folk.uib.no/ssu029/Pdf_file/Cuyt85.pdf). I've attached a
script, halley_method.mac, and halley_method.log, the output that I
get from running batch("halley_method.mac") in Maxima.

The final results appear to be the same for the 2 example problems in
the paper, but the per-iteration values are a little bit different. I
don't know if this is single precision vs double, or inaccuracies
induced by converting floats to rationals and back again (in Maxima),
or what.

The basic method is pretty simple, but the whole thing is obscured
somewhat by a layer of dross -- stuff like needing to convert a column
matrix to a list or vice versa and forcing values to be floats. I
don't know what could be done to make it clearer.

The iteration could be more efficient -- the LU decomposition of the
Jacobian is computed repeatedly. I didn't bother trying to save and
reuse any partial results but that's an obvious thing to do.

I'd be happy to hear questions or comments.

best,

Robert Dodier