f08utf computes a split Cholesky factorization of a complex Hermitian positive definite band matrix
. It is designed to be used in conjunction with
f08usf.
The factorization has the form
, where
is a band matrix of the same bandwidth as
and the following structure:
is upper triangular in the first
rows, and transposed — hence, lower triangular — in the remaining rows. For example, if
and
, then
None.
The computed factor
is the exact factor of a perturbed matrix
, where
is a modest linear function of
, and
is the
machine precision. It follows that
.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
A call to
f08utf may be followed by a call to
f08usf to solve the generalized eigenproblem
, where
and
are banded and
is positive definite.
The real analogue of this routine is
f08uff.