f07vgf estimates the condition number of a real triangular band matrix
, in either the
-norm or the
-norm:
The routine 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.
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 routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
A call to
f07vgf 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 (assuming
) but takes considerably longer than a call to
f07vef with one right-hand side, because extra care is taken to avoid overflow when
is approximately singular.
The complex analogue of this routine is
f07vuf.
This example estimates the condition number in the
-norm of the matrix
, where
Here
is treated as a lower triangular band matrix with one subdiagonal. The true condition number in the
-norm is
.