
204
K. Gallivan et al.
SinceM- Oand'~n aadTll areinvertible, wehave [T111Tla ] [ i X
= 0, which
yields,
AT.e = (~i~(~2. (32)
This establishes a new displacement identity where ~ and (~2 are obtained from (24-25).
3 BLOCK LOOK-AHEAD ALGORITHM
The above construction thus suggests the following algorithm for block Toeplitz matrices.
Algorithm 1 Block-Toeplitz
Construct generator
~(o), G(o)
Use Bunch Kaufman on To to obtain
To = U~EoUo
and define
0 -20 ' G(ol-" 0 EoU;-*T~ ... 2oUo*T~
Apply block Schur algorithm
i=l
while Gi-1 # void
Construct leading rows
[TIIIT~2 ]
from
E(i_x),
G(i-x)