Re: Searching zeros of complex function

From: Steven G. Kargl (kargl_at_c-67-168-59-70.client.comcast.net)
Date: 05/18/04 

Date: Tue, 18 May 2004 04:17:41 GMT

In article <7ccqc.13221$qJ5.352024@news20.bellglobal.com>,
        "Gerry Thomas" <gfthomas@sympatico.ca> writes:
>
> It's been known for a while: "Ueber unendlich viele Algorithmen zur
> Auslosung der Gleichungen," by E. Schroder, Math. Anal. (1870), and
> translated by G.W. Stewart. Steve Kargl's approach would appear to be
> related to Konig's theorem and is implicit in the use of the psuedospectra
> of the det of a matrix. It's a small world afterall!
>

I certainly won't claim that the approach I mentioned originated with
me. Indeed, many classic text on Complex Analysis from circa 1950/70
discuss the Winding Number theorem, the calculus of residues, and
Cauchy theorem. I haven't looked for earlier literature, but I suspect
that early atomic/nuclear/quantum physics used a similar approach
(e.g., in Regge Pole analysis). What is amazing to me, is that few
people seem to be aware that one can use contour integrals in the
complex plane to locate zeros a (complicated) functions. 

-- 
Steve

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