Thank you so much, Hoffrichter and Star Strider. I found out that there is a function called sylvester which can directly address the question.
How to solve matrix function in Matlab?
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Hi all! I'm faced with the following question:
X=AXB+C
where A is a 4*4 matrix, B is a 3*3 matrix, X and C are 4*3 matrices. I know the values of A, B and C. How can I solve out X using matlab?
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Star Strider
2021년 2월 21일
I considered that, however it does not appear to be a Sylvester system, at least as I interpret it. Another option I considered was lyap and its friends.
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Paul Hoffrichter
2021년 2월 21일
편집: Paul Hoffrichter
2021년 2월 21일
Define Z = AXB + C - X
You have to start off with your initial best guess for X based upon the nature of the model. For lack of any information, guess that X_0 = C. (Then Z = ACB.)
Create a Q = cost function for Z. You could try the trace of Z, and then check to see if Z has all entries close to 0.
You then need to find a zero crossing of your cost function. To do this, you can use fzero.
Other initial guesses may result in different answers if there are multiple roots.
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