Matrix-solution other than by Newton-Iteration?


Hi,

in the following matrix-problem

rA * (dX M dX M) = rB

where rA (row-vector), rB and M (matrix) are given,
dX (diagonal matrix) is sought.

Here I also know, that
rA = [1,a,a^2,a^3,...] , (and in this special case even rA=[1,1,1,1,...] )
rB = [1,b,b^2,b^3,...] and
dX = diag(1,x,x^2,x^3,...]

So in fact I only have a single unknown.
What I could try is simple iteration in the
sense of the scalar newton-iteration.

On the other hand, I could simplify a little bit:

I can put one inverse of M to the other side:

rA dX M dX = rB M^-1 = rC

and knowing rA = [1,1,1,1,...]

rX * M = rC dX^-1

But I think, this is not much helpful.

Any idea?

Thanks -

Gottfried
--

Gottfried Helms, Kassel
.