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Forums
Mathematics
General Math
Newton-Raphson Method With Complex Numbers
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[QUOTE="andrewkirk, post: 6843522, member: 265790"] For a complex function, for some initial guesses the method will not converge, see [URL='https://en.wikipedia.org/wiki/Newton%27s_method#Complex_functions']here[/URL]. If you know the real part of the domain, you'd likely have success by trying one initial guess in each connected component of that domain. But absent that knowledge, you can't do anything much. You could write a program to try to identify real parts of the domain, and then use those. But it might miss some, eg if they were very narrow. For instance the function: $$f(x) = 0.01 -\sqrt{0.01^2 - (x-10)^2}$$ is only real on ##[9.99, 10.01]## and has a single root 10. An algorithm searching for a region where the function is real could easily miss that small interval. [/QUOTE]
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Mathematics
General Math
Newton-Raphson Method With Complex Numbers
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