Re: Muller's method code ?

From: Steven G. Kargl (kargl_at_troutmask.apl.washington.edu)
Date: 02/22/05 

Date: Tue, 22 Feb 2005 00:14:30 +0000 (UTC)

In article <cvds9j$ef4$1@scrotar.nss.udel.edu>,
        Rich Townsend <rhdt@barVOIDtol.udel.edu> writes:
>
> Madhusudan Singh wrote:
>>
>> As a part of a problem I am solving, I need to find all the zeroes of a
>> complex function. I have found (through Google) that Muller's method is the
>> method of choice for this problem.
>>
>> Though I have found the algorithm for real variables on mathworld :
>>
>> http://mathworld.wolfram.com/MullersMethod.html,
>>
>> I want to save myself some coding/debugging time. So, I was wondering if
>> someone knows of a URL for this algorithm coded in Fortran 77/95.
>>
>
> I attach my own implementation of Muller's method for complex variables,
> based on Traub's implementation of the algorithm ("Iterative Methods for
> the Solution of Equations", Prentice-Hall, Englewood Cliffs). I've found
> that this routine works well, and appears to be robust.
>
> A couple of points:
>
> 1) Muller's method is not guaranteed to find all roots; it is only as
> good as the starting guesses you pass in z_1, z_2 and z_3; furthermore,
> there is no guarantee that all roots have been found. This relates to
> the larger problem that there is no sure-fire way of finding out how
> many roots actually exist.

Well, you can determine the number of zeros (and poles) within
a closed contour by computing the winding number integral. You
can make the closed contour as large as you want provided it
does not cross a branch cut or include a zero or pole on the
contour itself. 

-- 
Steve
http://troutmask.apl.washington.edu/~kargl/

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