328
APPENDIX B LDL t Factorization and Constrained Linear
Systems
(8)
-1 B 1
B t A B t
1 B -1
c
b ,
c
that is,
two
Lagrange multipliers instead of one. The matrix of (8) is
indeed LDLt-factorizable, under the above hypotheses"
-1 B 1 1 -1 1 -B -1
B t
A
B t
-- -B t 1 A + BtB
1 2~ t ,
1 B -1 -1 2[5 1 -4y 1
with the same [3 and Y as above. So one can solve (5) this way, by
running an LDL t package on (8). But the numerical effort involved is no
less than was required by the above method (a bit
more,
actually, since
some arithmetic is wasted on numerically retrieving the first column
block of L, that is {1,-
B t, - 1},
which is already known). As the
heuristic leading from (5) to (8) is quite obscure, in comparison with the
easily motivated passage from (5) to (6), this "double-multiplier" approach
is more of a curiosity than a real alternative. 0
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[AHI
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[cc]
[GL]
[Kn]
[MW]
[Me]
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