NAG Library Routine Document
F08JFF (DSTERF) computes all the eigenvalues of a real symmetric tridiagonal matrix.
The routine may be called by its
F08JFF (DSTERF) computes all the eigenvalues of a real symmetric tridiagonal matrix, using a square-root-free variant of the algorithm.
The routine uses an explicit shift, and, like F08JEF (DSTEQR)
, switches between the
variants in order to handle graded matrices effectively (see Greenbaum and Dongarra (1980)
Greenbaum A and Dongarra J J (1980) Experiments with QR/QL methods for the symmetric triangular eigenproblem LAPACK Working Note No. 17 (Technical Report CS-89-92)
University of Tennessee, Knoxville http://www.netlib.org/lapack/lawnspdf/lawn17.pdf
Parlett B N (1998) The Symmetric Eigenvalue Problem SIAM, Philadelphia
- 1: – INTEGERInput
On entry: , the order of the matrix .
- 2: – REAL (KIND=nag_wp) arrayInput/Output
the dimension of the array D
must be at least
On entry: the diagonal elements of the tridiagonal matrix .
eigenvalues in ascending order, unless
(in which case see Section 6
- 3: – REAL (KIND=nag_wp) arrayInput/Output
the dimension of the array E
must be at least
On entry: the off-diagonal elements of the tridiagonal matrix .
- 4: – 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 algorithm has failed to find all the eigenvalues after a total of
, then on exit
elements of E
have not converged to zero.
The computed eigenvalues are exact for a nearby matrix
is the machine precision
is an exact eigenvalue and
is the corresponding computed value, then
is a modestly increasing function of
8 Parallelism and Performance
F08JFF (DSTERF) is not threaded in any implementation.
The total number of floating-point operations is typically about , but depends on how rapidly the algorithm converges. The operations are all performed in scalar mode.
There is no complex analogue of this routine.
This example computes all the eigenvalues of the symmetric tridiagonal matrix
10.1 Program Text
Program Text (f08jffe.f90)
10.2 Program Data
Program Data (f08jffe.d)
10.3 Program Results
Program Results (f08jffe.r)