Re: System of equations with complex numbers

On 26 Apr 2006 20:53:14 -0700, diltsman@xxxxxxxxx wrote:

As far as arithmatic goes, at least for matrix multiplication, it is
O(n^3), so it takes a lot more computations.

It's not that bad. If we start with an n x n matrix of complex numbers
and transform it to a 2n x 2n pure real matrix, remember that the n x n
complex matrix will take 4 multiplies and 2 adds whenever we need to
multiply two elements, but the larger 2n x 2n matrix will only require a
single multiply per each (and, of course, there is some more arithmetic
besides just this).

I'm comparing the 2n x 2n pure real case with the n x n complex case, and
for a square matrix, the ratio is not as great as 2^3, but I don't feel
like figuring out just what it is. :-)


Rodger Rosenbaum wrote:
On Wed, 26 Apr 2006 12:54:22 -0700, "Joel Kolstad"
<JKolstad71HatesSpam@xxxxxxxxx> wrote:

Rodger,

Could you comment on the limitations or implications of solving a complex
system of equations by building a block matrix out of Re(A) and Im(A) like I
suggested to the original poster?

Thanks,
---Joel

The technique I am aware of replaces each complex number c with a 2x2
real block matrix like this:

[[ RE(c) -IM(c) ]
[ IM(c) RE(c) ]]

This causes each n x m matrix to become a 2n x 2m matrix. The complex
numbers of the result can be read as the first column of each 2x2 block in
the overall result matrix.

The required storage is doubled and I think the arithmetic is (at least)
doubled, too.

The HP71's math pack used this technique for its complex matrix
operations, AFAIK.

.

Relevant Pages

  • Re: System of equations with complex numbers
    ... As far as arithmatic goes, at least for matrix multiplication, it is ... Rodger Rosenbaum wrote: ... system of equations by building a block matrix out of Reand Imlike I ... The technique I am aware of replaces each complex number c with a 2x2 ...
    (comp.sys.hp48)
  • Re: System of equations with complex numbers
    ... Could you comment on the limitations or implications of solving a complex ... system of equations by building a block matrix out of Reand Imlike I ... The technique I am aware of replaces each complex number c with a 2x2 ...
    (comp.sys.hp48)