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 https://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: – doubleInput/Output
Note: the dimension, dim, of the array d
must be at least
On entry: the diagonal elements of the tridiagonal matrix .
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
The algorithm has failed to find all the eigenvalues after a total of iterations; elements of e have not converged to zero.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
The computed eigenvalues are exact for a nearby matrix , where
and is the machine precision.
If is an exact eigenvalue and is the corresponding computed value, then
where is a modestly increasing function of .
8Parallelism and Performance
f08jfc 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 function.
This example computes all the eigenvalues of the symmetric tridiagonal matrix , where