eigen value vs Newton's Method vs.... also Matlab Symbolic Toolkit

eigen value vs Newton's Method vs.... also Matlab Symbolic Toolkit

Post by Richard Fatema » Thu, 22 May 2003 03:34:55



The Numerical Algorithms Group (NAG) does this kind of thing for
a living; they have a Laguerre method as their primary algorithm
it seems.

http://www.nag.com/numeric/FL/manual/pdf/C02/c02_intro.pdf

I would not be surprised if Matlab previously had a Jenkins-Traub
algorithm and discarded it.

The Matlab symbolic toolkit, since you mention it, is something
I have been playing with. And I think it is more appropriate
to discuss that here, since it is peripheral to most Matlab
activities.

In order to convert a Matlab value to a symbolic one, you can
add sym(0) to it.
Thus
simplify(3+sym(0))  is ok, and returns 3.  While simplify(3) is
illegal: an attempt to call a symbolic routine "simplify" on a
traditional Matlab value, the 1X1 array of double-precision numbers,
namely  3.    This is a misfeature, certainly. Why not add sym(0)
and see what happens instead of the mysterious error message.

But here is an anomaly...

simplify(pi^2+sym(1))   returns a number 3059521645650671/281474976710656
but
simplify(pi+sym(1))  returns  pi+1

Cheers..
RJF


> If you and/or the original poster would like to suggest that MATLAB use
> these algorithms for polynomial root finding instead of or in addition to
> the routine currently used in roots.m, please suggest it to

> future version of MATLAB.  Also (to the original poster) while sometimes
> questions about MATLAB's Symbolic Math Toolbox are posted to
> sci.math.symbolic, you're more likely to get a discussion about MATLAB going
> on the MATLAB newsgroup comp.soft-sys.matlab.

> --
> Steve Lord


 
 
 

1. eigen value vs Newton's Method

I'll give more details and some limitations later
(I had a detailed mail when netscape crashed;
now I have to reconstruct everything I wrote...)

Since you are from Mathworks, why don't you suggest it to them?

I have bad experience with suggesting changes to the Matlab team.
None of several suggestions had any effect. For example,
many years ago I mentioned that fzero fails to solve a simple
quadratic equation. But it still does, as anyone can see who tries
   x=fzero('x^2-0.009',1)
(The reply I got from Mathworks was that it works with a different
starting value!)
There are a number of very simple remedies, one of them being described
in my recent numerical analysis book
http://www.mat.univie.ac.at/~neum/index.html#numbook
[~ is a tilde]

Arnold Neumaier

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