
272
F. Vanpoucke et al.
/' in
/__I_L-~ /'__I_E-~ / X out
/ /" i
1
/
,"
out
~' ...,"1~ '
/'1~ /
z~"'
i
(r-a~ /, ''-ff
./~-~ L
Xl x2 x3 x4
2•qut
3
= QilJ T .
in]
xi
in
zj
Figure 2" SFG of the factored orthogonal matrix-vector multiplication (M = 4).
3 UPDATING THE ANGLES
In step 3 of Algorithm 1, the
V[k_l] matrix
is post-multiplied by a sequence of M- 1 Givens
9 ili+x ,~ilj
rotations r . In this section we present an
O(M 2)
method to update the angles ~'[k-1]
directly, without explicit computation of the V-matrix.
The updating matrix 1 (~ is the product of rotations on neighboring