F08UFF (DPBSTF) computes a split Cholesky factorization of a real symmetric positive definite band matrix.
F08UFF (DPBSTF) computes a split Cholesky factorization of a real symmetric positive definite band matrix
B. It is designed to be used in conjunction with
F08UEF (DSBGST).
The factorization has the form
B=STS, where
S is a band matrix of the same bandwidth as
B and the following structure:
S is upper triangular in the first
n+k/2 rows, and transposed — hence, lower triangular — in the remaining rows. For example, if
n=9 and
k=2, then
None.
The computed factor
S is the exact factor of a perturbed matrix
B+E, where
ck+1 is a modest linear function of
k+1, and
ε is the
machine precision. It follows that
eij≤ck+1εbiibjj.
A call to F08UFF (DPBSTF) may be followed by a call to
F08UEF (DSBGST) to solve the generalized eigenproblem
Az=λBz, where
A and
B are banded and
B is positive definite.
The complex analogue of this routine is
F08UTF (ZPBSTF).