NAG Library Routine Document
F07JGF (DPTCON) computes the reciprocal condition number of a real
symmetric positive definite tridiagonal matrix
, using the
factorization returned by F07JDF (DPTTRF)
||D(*), E(*), ANORM, RCOND, WORK(N)
The routine may be called by its
F07JGF (DPTCON) should be preceded by a call to F07JDF (DPTTRF)
, which computes a modified Cholesky factorization of the matrix
is a unit lower bidiagonal matrix and
is a diagonal matrix, with positive diagonal elements. F07JGF (DPTCON) 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
Higham N J (2002) Accuracy and Stability of Numerical Algorithms (2nd Edition) SIAM, Philadelphia
- 1: – INTEGERInput
On entry: , the order of the matrix .
- 2: – REAL (KIND=nag_wp) arrayInput
the dimension of the array D
must be at least
On entry: must contain the diagonal elements of the diagonal matrix from the factorization of .
- 3: – REAL (KIND=nag_wp) arrayInput
the dimension of the array E
must be at least
: must contain the
subdiagonal elements of the unit lower bidiagonal matrix
can also be regarded as the superdiagonal of the unit upper bidiagonal matrix
- 4: – REAL (KIND=nag_wp)Input
-norm of the original
, which may be computed by calling F06RPF
with its parameter
must be computed either before
calling F07JDF (DPTTRF)
or else from a copy
of the original matrix
- 5: – REAL (KIND=nag_wp)Output
On exit: the reciprocal condition number, .
- 6: – REAL (KIND=nag_wp) arrayWorkspace
- 7: – INTEGEROutput
unless the routine detects an error (see Section 6
6 Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The computed condition number will be the exact condition number for a closely neighbouring matrix.
8 Parallelism and Performance
The condition number estimation requires floating-point operations.
See Section 15.6 of Higham (2002)
for further details on computing the condition number of tridiagonal matrices.
The complex analogue of this routine is F07JUF (ZPTCON)
This example computes the condition number of the symmetric positive definite tridiagonal matrix
10.1 Program Text
Program Text (f07jgfe.f90)
10.2 Program Data
Program Data (f07jgfe.d)
10.3 Program Results
Program Results (f07jgfe.r)