In particular, the X matrices defined in the document are of size $(I+1)\times I$ and $(2 I + 1)\times 2I$, but the rank of them is $I$ and $2I$. This means that the overdetermined system can be solved as a linear system. The rank can be checked with an SVD or the rank function of matlab. The fact that this is really a system should be pointed out in the document prior to describing it as a LLS problem.
On the other hand, this doesn't necessarily change the solution technique for the system. For dense setups, the LLS approach can be compared to doing a pseudo-inverse or something similar in speed - but I suspect that LLS is close enough.
For sparse systems, we could investigate whether there are any sparse direct solvers that can solve rectangular systems. Iterative methods wouldn't work, but gaussian elimination should. Alternatively it is possible that sparse LLS is the best approach even if the rank is known.
In particular, the X matrices defined in the document are of size $(I+1)\times I$ and $(2 I + 1)\times 2I$, but the rank of them is $I$ and $2I$. This means that the overdetermined system can be solved as a linear system. The rank can be checked with an SVD or the
rankfunction of matlab. The fact that this is really a system should be pointed out in the document prior to describing it as a LLS problem.On the other hand, this doesn't necessarily change the solution technique for the system. For dense setups, the LLS approach can be compared to doing a pseudo-inverse or something similar in speed - but I suspect that LLS is close enough.
For sparse systems, we could investigate whether there are any sparse direct solvers that can solve rectangular systems. Iterative methods wouldn't work, but gaussian elimination should. Alternatively it is possible that sparse LLS is the best approach even if the rank is known.