> Beyond what is available in the API (Q and R), what exactly does the
> QR Decomp "know" that makes solving easier?
It has Q stored as a list of Householder vectors. Multiplying a matrix
with Q or Q' that is stored in this format is not much more expensive
than a normal matrix multiplication, but it's a lot more efficient
when compared to first calculating an explicit form of Q and then
multiplying. It might be better numerically too, but I cannot be sure.
Yes, QR is better, although it is more expensive to solve from scratch,
because of the ortogonality of the Q matrix.
It is particulary good for not very well conditioned systems. Sometimes you
can't even solve with LU, but you can with QR.
Vanessa
