F07JRF (ZPTTRF) factorizes the matrix
A
as
where
L
is a unit lower bidiagonal matrix and
D
is a diagonal matrix with positive diagonal elements. The factorization may also be regarded as having the form
UHDU
, where
U
is a unit upper bidiagonal matrix.
None.
The computed factorization satisfies an equation of the form
where
and
ε
is the
machine precision.
Following the use of this routine,
F07JSF (ZPTTRS) can be used to solve systems of equations
AX=B
, and
F07JUF (ZPTCON) can be used to estimate the condition number of
A
.
The real analogue of this routine is
F07JDF (DPTTRF).
This example factorizes the Hermitian positive definite tridiagonal matrix
A
given by