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Topic: f(z) + abs(z) = 0, where z is complex
Replies: 18   Last Post: Jul 11, 2011 9:23 AM

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Thomas Koenig

Posts: 5
Registered: 12/15/08
Re: f(z) + abs(z) = 0, where z is complex
Posted: Jul 10, 2011 3:16 PM
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slawek <human@site.pl> schrieb:
> I am looking for a numerical solution of f(z) + abs(z) = 0, where z is a
> complex number and f is the analytic function.
>
> Newton method does not work, because there is no derivative of the
> non-analytic abs(z).


Take z = x + I*y, split f(x) into its real part f1(x,y) and its
imaginary part I*f2(x,y), then calculate the zeros of the
functions

f1(x,y) - sqrt(x^2+y^2)
f2(x,y)

using a two-dimensional Newton method.



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