Re: Roots of equations Was: Newton Raphsons iteration method

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#405

From: Steven Smith
Date: Wed, 02 Sep 1992 15:37

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alex@iastate.edu (Roger Alexander) writes:

>          Not so.  The solutions of the equation are isolated (implicit
> function theorem) but there may be infinitely many.  Let
>
>          g(x,y) = (exp(x)cos(y)-1, exp(x) sin(y)).
>
> Then det g' = exp(2x) != 0 anywhere, but g(0,2*Pi*n) = 0 for every
> integer n.

Yes, I posted before I thought.  The example x -> sin x works too.
The zero set of an analytic function !==0 is at most countable.

Steven Smith

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Path: arc1-ca.pugleaf.net!sparky!uunet!ogicse!das-news.harvard.edu!das-news!smith
From: smith@minerva.harvard.edu (Steven Smith)
Newsgroups: sci.math.num-analysis
Subject: Re: Roots of equations Was: Newton Raphsons iteration method
Message-ID: <SMITH.92Sep2103757@minerva.harvard.edu>
Date: 2 Sep 92 15:37:57 GMT
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