🚀 go-pugleaf

The equation that I have is

A x + m z = b

where m is a real scalar and all others have complex elements.

A is a square matrix, b, x are column vectors. x is the vector 
to be solved for and the elements of z are related to those of 
x by zi=xi/magnitude(xi) where xi and zi are the i th elements 
of x and z respectively. In addition, A is a hermitian matrix. 

The dimensions of the above matrices are very small (could be
as low as 2). 

What kind of methods can I use to solve this problem? I
know this can be solved by least squares method. But  
are there any numerical routines which can give all the
solutions? If yes, what are they and where do I get them?

I am not very well-versed with numerical methods so any
references in this regard would also be helpful. (Can this
problem be solved analytically?)

Thank you,

Sarath.
sarath@pender.ee.upenn.edu

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P. Sarath Kumar      314, Moore School, 200 S.33rd St.,  Philadelphia, PA19104.
		     Ph: Off (215)-898-4183.  Res: (215)-387-1880.

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