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This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".
3
votes
Invert a matrix only on a subset of variables / Compute the "equivalent circuit"
The procedure you need to get the "reduced" equations is often referred to as "static condensation" in the FEM literature. You can
partition your FE equations as follows:
$$
\left[\begin{array}{cc}
…
2
votes
Solve $AX=B$ where $A$ is a skyline matrix
The matrix in your case 2 example has a much higher condition number than the one in the original 5-equation example. Accordingly, errors in the definition of the matrix terms result in larger errors …