F07JDF (DPTTRF) 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
UTDU
, 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,
F07JEF (DPTTRS) can be used to solve systems of equations
AX=B
, and
F07JGF (DPTCON) can be used to estimate the condition number of
A
.
The complex analogue of this routine is
F07JRF (ZPTTRF).
This example factorizes the symmetric positive definite tridiagonal matrix
A
given by