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2

If I understand correctly, you want numpy.kron.


5

This is more generally known as the distance geometry problem where we are trying to reconstruct data points given distances between all or some of the points with respect to some distance metric. A common application for $D=3$ is in chemistry/biology where certain experimental techniques can help determine the distance between atoms and the goal is to ...


4

I do not know anything about the specific problem, but you might want to look into the techniques the "SParse Approximate Inverse (SPAI)" community has come up with over the past two decades. There, one is looking for a matrix $B \approx A^{-1}$ so that $\|BA-I\|$ is minimized (with regard to some norm, typically the Frobenius norm) and requiring ...


3

One reason why there might not be much research on this is that one usually avoids sparse matrix multiplications as much as possible in the first place. When applying the product to a vector $ABv$, you can associate from the right $A(Bv)$, and when solving linear systems you can add auxiliary variables to avoid forming the product; for instance, turn $c = ...


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