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J.L. Barlow et al.
5. (Restore lower triangular form ) Find an orthogonal matrix ~d2 such that
Is~)r o ther~
( 0o) (L3 0 0)
g'= P d~ o = F(3) G(4) 0 .
0 0 0 0 0 0
~r = diag(Ik, ~, In-p)diag(V2, In-p)
Go to step 7 else go to step 6.
a.
(Reduce G fu~the~ if ~ingul~) II g~)= 0
th~
S~)= 0
at~o ,~.c~ it ~a~ Io~m~
from g~) using V2. Thus
k
p-k
(L30) k
F(3) G(4) = 1 0 0
p- k - 1 p ~(4)
k p-k k 1 p-k-1
(~(4) is a lower Hessenberg matrix. We then find an orthogonal matrix fr3 such that
n-k-1 1
If we place the zero row at the end, C has the form
C=
k ( 00)
p-k-1