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On Wed, 19 Aug 2009, Benoit Jacob wrote:
I was intrigued by the option of computing/storing only the sequence
of Givens rotations, which doesn't seem like common practice at all; i
was expecting a GivensQR class to compute/store Q and/or R according
to what the user asked for.
The HouseholderQR class does something similar. It doesn't store Q but
only the sequence of Householder reflections. The matrix Q is only
computed when the user asks for it.
So I wondered what was the use case for the approach of storing the
sequence of Givens rotations, and it seems to me that the best use
case for it should be when doing only 1 vector solve. Indeed, in that
case, avoiding the overhead of computing Q or R should be the most
Another use case is solving an overdetermined system in the least-square
sense. You don't need to compute Q; you only need to be able to multiply Q
with a vector.