Their value is used for the value of other elements.
If I got your idea right, their value won’t cripple into other elements.
Indeed, the original problem is given by:
\begin{bmatrix} \boldsymbol{A} \\ \boldsymbol{E} \end{bmatrix} \begin{bmatrix} \boldsymbol{x}_{\mathcal{U}} \\ \boldsymbol{x}_{\mathcal{V}} \end{bmatrix} = \begin{bmatrix} 0 \\ \boldsymbol{x}_{\mathcal{V}} \end{bmatrix}
Where:
- \boldsymbol{E} = \begin{bmatrix} \boldsymbol{0} & \boldsymbol{I} \end{bmatrix}.
- \mathcal{U} = \left\{ 1, 2, \ldots, n \right\} \setminus \mathcal{V}.
But it is a larger system (n \times n) which is neither symmetric nor PSD. I thought it would be slower to solve.
Does the solvers will be able to take advantage of its structure?
Maybe I need to build a specialized operator?
I just thought in literature there are optimized solvers or approaches for such structure.