Does Matlab automatically detect "psychologically" lower triangular matrices when solving Ax=b?
I.e. if you do an lu decomposition to get a (permuted) L and an upper triangular U, and solve the system explicitly with something like:
[L,U] = lu(A)
x = U\(L\b)
Does Matlab "know" that when solving L\b, L is a (permuted) lower triangular, and take advantage of that?
If so, how does it detect that? Note that in this case the "P" orthognal permutation is not exported.
BTW: I'm glad the help file has removed the "psychologically" term, I never thought that helped understanding in the slightest.