184
the Bunch-Kaufman pivoting [6, §4.4]). The algorithm is formulated in [4,
6, 13, 17]. As a,
result we get
PAP
T
=
LDL
T
.
where
L is unit lower triangular,
D is block diagonal with 1×1, or 2×2
blocks, and
P is a permutation matrix.
Now let us look at a recursive formulation of this algorithm. This is
given below. The recursion is done on the second dimension of matrix
A,
i.e. the algorithm works
on full columns like in the LU factorization.
The LAWRA project on
LDL
T
is still going on. We have developed
several perturbation approach algorithms for solving
linear systems of equa-
tions, where the matrix is symmetric and indefinite. The results are pre-
sented in two papers, [7, 12].
We have also obtained very good results for the Bunch-Kaufman fac-
torization, where the matrix
A is given in packed data format with about 5%
extra space appended. We call it a blocked version. The recursion is not
applied. The speed of our packed blocked algorithm is comparable with the
speed of LAPACK full storage algorithm. The algorithm is described and
the comparison performance results for the factorization
and solution are
presented in [11].
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