f08utc computes a split Cholesky factorization of a complex Hermitian positive definite band matrix
. It is designed to be used in conjunction with
f08usc.
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 function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
A call to
f08utc may be followed by a call to
f08usc to solve the generalized eigenproblem
, where
and
are banded and
is positive definite.
The real analogue of this function is
f08ufc.