There have been several recent developments on the "root finding
problem" (variations of Newton's method for approximate roots).
In particular, a paper of Hubbard-Schleicher-Sutherland presents an
algorithm to find all roots of a complex polynomial with a reasonable
number of steps.
For general variations and improvements of Newton's method, I have put some
papers on the web site of a course I am teaching.
Check out the papers by Shub-Smale, Hubbard-Schleicher-Sutherland, and
Schleicher in Section 14 of
http://janus.math.msu.edu/sen/WWW/Math_840/
Perhaps it would be interesting for someone to implement some of the
new methods in maxima, say the Shub-Smale method or the
Hubbard-Schleicher-Sutherland method.
FWIW,
-sen
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| Sheldon E. Newhouse | e-mail: sen1 at math.msu.edu |
| Mathematics Department | |
| Michigan State University | telephone: 517-355-9684 |
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On Mon, 19 Mar 2007, Robert Dodier wrote:
> On 3/19/07, Alasdair McAndrew <amca01 at gmail.com> wrote:
>
>> Does Maxima implement any general method of solving these? There are a few
>> Newton's methods, but is that all? Is there a Brent's method in there
>> somewhere, or a Broyden's method for systems, for example? Should I write
>> some?
>
> Aside from Newton's method, there are no other algorithms to solve
> nonlinear or nonpolynomial systems of equations in Maxima
> (so far as I know). If you or your students want to work on that,
> that would be terrific. Maybe a workable place to start is the
> Fortan code at Netlib. Fortran can be translated automatically
> to Lisp via the f2cl program.
>
> FWIW
> Robert
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