Re: [Algorithms] solving for multiple matrices

[David B. <dbe...@na...>]

This is just a shot in the dark, but the wikipedia entry on "QZ decomposition" looks a lot like your original statement of the problem --
http://en.wikipedia.org/wiki/Matrix_decomposition#QZ_decomposition

I don't know if X & Y are "unitary" matrices though.  I guess that depends on which kinds of transforms you are using.

Hope that helps,

David Bennett
NAMCO BANDAI Games America Inc.


-----Original Message-----
From: Andras Balogh [mailto:and...@gm...]
Sent: Thursday, September 17, 2009 12:38 PM
To: gda...@li...
Subject: [Algorithms] solving for multiple matrices

Hi, I have a chain of transformations with multiple unknown (but fixed!) transforms. What I do know is the end result transformation and some of the transformations in between, and I know these for multiple frames. So
  from here, I'd like to compute the unknowns. Here it is in more formal
version:

I'd like to find 2 unknown matrices X and Y. I have 4 known matrices A1, A2, B1 and B2, and also know this:
A1 = X * B1 * Y
A2 = X * B2 * Y

I can compute X from the first equation:
X = A1 * Y^-1 * B1^-1

And substitute it into the second:
A2 = A1 * Y^-1 * B1^-1 * B2 * y

Assigning:
C = A1^-1 * A2
D = B1^-1 * B2

Then it becomes:
C = Y^-1 * D * Y

Now, how do I solve this for Y? This form lookes strangely familiar, but I cannot figure out what to do from here (wish I knew how to Google this ;).
Hopefully there's an analytic solution to this. Any ideas?

Thanks,



Andras

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