I have a matrix equation of the form
$$ Q=SBS+SBA+HSBZ+ABS+ABA+ABZ+ZBS+ZBA+ZBZ. $$
If it weren't for the $H$ matrix in the third term, the whole thing would be
$$ Q^\prime=(S+A+Z)B(S+A+Z). $$
As it is, I was able to reduce it to
$$ Q=(S+A+Z)B(S+A+Z)+(H-I)SBZ, $$ but I want to eliminate the addition, if possible. In other words, I am looking for an expression like
$$ Q=f(S,A,H,Z)Bg(S,A,H,Z), $$ where $f(.)$ and $g(.)$ are matrix functions.
All matrices are square and real. $S$ is symmetric and $H$ is a diagonal.
I am looking for some $f(.)$ and $g(.)$. I will be calculating $$ Q^{(n)}=f^n(S,A,H,Z) B g^n(S,A,H,Z), $$ and I will be using SVD to proceed. Thus eliminating the addition helps me a lot.
Thanks!