F07VUF (ZTBCON) estimates the condition number of a complex triangular band matrix.
F07VUF (ZTBCON) estimates the condition number of a complex 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.
A call to F07VUF (ZTBCON) involves solving a number of systems of linear equations of the form
or
; the number is usually
and never more than
. Each solution involves approximately
real floating point operations (assuming
) but takes considerably longer than a call to
F07VSF (ZTBTRS) with one right-hand side, because extra care is taken to avoid overflow when
is approximately singular.
The real analogue of this routine is
F07VGF (DTBCON).
This example estimates the condition number in the
-norm of the matrix
, where
Here
is treated as a lower triangular band matrix with two subdiagonals. The true condition number in the
-norm is
.