Questions about QR blocked algorithm described in # 191

[linyufly]

As far as I am concerned, given m >= n, the result of QR(A_m,n) would be V_m,n T_n,n and R_m,n.

In LAPACK Working Note # 191, the DTSQRT is described below:

( Rkk) (Rkk)
( ) -----> (Vik, Tik, Rkk) = QR( )
( Aik ) (Aik )

Since the coupling of Rkk and Aik is a (2b)X(b) block, I think m = 2b and n = b here. Therefore I think Vik and Rkk are no longer bXb blocks but (2b)X(b). How can these blocks fit into original matrix? For Rkk, maybe we can just ignore the lower bXb zero block. But I don't think we can do the same thing for Vik.

Thank you!

[ltaief]

The size of Vik is indeed (2b)x(b). The lower part of size bxb contains the
computed reflectors and the upper part of size bxb is the Identity matrix
which does not need, therefore, to be stored.
Hope this helps!
Hatem