These are chat archives for elemental/chat

1st
Apr 2017
Jack Poulson
@poulson
Apr 01 2017 15:24
it doesn't, but Tikhonov does
at least, dense least squares doesn't
or, to be more specific, the height >= width case solves min_x || A x - b ||_2, which doesn't bound the norm of x
the height < width case solves min_x || x ||_2 s.t. A x = b
Tikhonov is a good middle-ground
Ryan H. Lewis
@rhl-
Apr 01 2017 16:36
What happens if A is rank deficient in the tall and skinny case ?
Ryan H. Lewis
@rhl-
Apr 01 2017 16:43
Also along similar lines Is the QR factorization a strong rrqr ?
Jack Poulson
@poulson
Apr 01 2017 18:47
for Tikhonov you end up with the solution to min_x || A x - b ||_2^2 + gamma || x ||_2^2
A being rank-deficient is irrelevant
is which QR factorization strong RRQR?
no one ever implements strong RRQR
Businger-Golub is just as good except for very pathological examples
and the randomized column-pivoted QR is good in even more situations