Nj. Higham, FACTORIZING COMPLEX SYMMETRICAL MATRICES WITH POSITIVE-DEFINITE REAL AND IMAGINARY PARTS, Mathematics of computation, 67(224), 1998, pp. 1591-1599
Complex symmetric matrices whose real and imaginary parts are positive
definite are shown to have a growth factor bounded by 2 for LU factor
ization. This result adds to the classes of matrix for which it is kno
wn to be safe not to pivot in LU factorization. Block LDLT factorizati
on with the pivoting strategy of Bunch and Kaufman is also considered,
and it is shown that for such matrices only 1 x 1 pivots are used and
the same growth factor bound of 2 holds, but that interchanges that d
estroy band structure may be made. The latter results hold whether the
pivoting strategy uses the usual absolute value or the modification e
mployed in LINPACK and LAPACK.