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In my research, I need to solve a matrix equation very similar to Lyapunov equation but with one extra term.

The equation is X+DXD-WXW=A, where X is the unknown n*n matrix. W, D and A is known. W is a symmetric n*n matrix, A is not symmetric. D is an diagonal matrix, and D and W cannot commute. So DXD is an extra term the original Lyapunov equation.

So may I ask whether this equation or its analogue has been studied in the literature? My difficulty is since D and W cannot commute, I cannot perform a simultanenous triangularization for D and W.

Thank you very much for your help!

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    Check also the literature for " Generalized Sylvester Equations", you might find something useful.2012-10-30

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