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[Lapack] Question about matrix equations

Dear Sir/Madam:

I am a postdoc working on biomedical imaging at Harvard Medical School. I came 
across a problem seemed related to Sylvester equations during optimizing my 
experimental setup.

I searched online and found LAPACK library on your website. So I am writing 
this email seeking your help.

-----------------------------------
All are 2*2 matrices with complex values (all are nonzero)
P1 and P2 : known with small errors
Q1 and Q2 : known with small errors
X and Y: unknown

X?P1?Y = Q1
X?P2?Y = Q2

It seems a generalized Sylvester equation (with G=H=0) 
AX-YB = G
EX-YF = H
---------------------------------------

I am just wondering whether it is solvable by using "ZTGSYL.f"in LAPACK.
http://www.netlib.org/lapack/complex16/ztgsyl.f
 
Thanks a lot in advance,
Kind Regards,

Ellen

(Ellen) Ziyi Zhang
Research fellow
Harvard Medical School
Wellman Center for Photomedicine
Massachusetts General Hospital
40 Blossom St., Barlett Hall 722
Boston, MA 02114
Tel: 617-726-0157
Fax: 617-726-4103
Email: zzhang0@Domain.Removed



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