nag_dtpcon (f07ugc) estimates the condition number of a real triangular matrix, using packed storage.
nag_dtpcon (f07ugc) estimates the condition number of a real triangular matrix
, in either the
-norm or the
-norm, using packed storage:
The function computes
or
exactly, and uses Higham's implementation of Hager's method (see
Higham (1988)) to estimate
or
.
Higham N J (1988) FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation ACM Trans. Math. Software 14 381–396
The computed estimate
rcond is never less than the true value
, and in practice is nearly always less than
, although examples can be constructed where
rcond is much larger.
nag_dtpcon (f07ugc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
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 nag_dtpcon (f07ugc) involves solving a number of systems of linear equations of the form
or
; the number is usually
or
and never more than
. Each solution involves approximately
floating-point operations but takes considerably longer than a call to
nag_dtptrs (f07uec) with one right-hand side, because extra care is taken to avoid overflow when
is approximately singular.
The complex analogue of this function is
nag_ztpcon (f07uuc).
This example estimates the condition number in the
-norm of the matrix
, where
using packed storage. The true condition number in the
-norm is
.