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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 ...


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 ...


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 ...


$A^{-1}B$ 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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