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2

Most of this was already discussed in the comments, but I would like to elaborate and put a detailed answer. There are no elementary characteristics (definiteness, symmetry, bandwidth) which can tell you whether the underlying (mixed or not) FEM/FVM is stable to solve the continuous problem. You can not tell anything about that just by looking at those ...

0

You can and should solve this problem without linear programming and apply the Bellman equation instead. Actually, the minmax theorem -- handled numerically via LP -- is only required to solve the problem where both players simultaneously choose an action. In contrast, your game consists of a two-step process, and the mathematical model should incorporate ...

2

Unfortunately, the problem as stated is not quite restrictive enough to meaningfully exploit. For any "interesting" sparse matrix $\mathbf A$, even if the forcing data $\mathbf b$ is sparse, the solution data $\mathbf x$ will still be fully populated/dense. However, there is a nearby problem that does have exploitable structure: if $\mathbf b$ is ...

3

$A^{-1}B$ is a $2\cdot 10^5 \times 1\cdot 10^6$ matrix that is likely to be full, so the size of your output is 1.6 TB. I don't think you have other alternatives than writing it to the disk.

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