nag_zptcon (f07juc) computes the reciprocal condition number of a complex
by
Hermitian positive definite tridiagonal matrix
, using the
factorization returned by
nag_zpttrf (f07jrc).
nag_zptcon (f07juc) should be preceded by a call to
nag_zpttrf (f07jrc), which computes a modified Cholesky factorization of the matrix
as
where
is a unit lower bidiagonal matrix and
is a diagonal matrix, with positive diagonal elements.
nag_zptcon (f07juc) then utilizes the factorization to compute
by a direct method, from which the reciprocal of the condition number of
,
is computed as
is returned, rather than
, since when
is singular
is infinite.
The computed condition number will be the exact condition number for a closely neighbouring matrix.
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.
See Section 15.6 of
Higham (2002) for further details on computing the condition number of tridiagonal matrices.
The real analogue of this function is
nag_dptcon (f07jgc).
This example computes the condition number of the Hermitian positive definite tridiagonal matrix
given by