SLARRJ
June 2010
Purpose
Given the initial eigenvalue approximations of T, SLARRJ
does bisection to refine the eigenvalues of T,
W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
guesses for these eigenvalues are input in W, the corresponding estimate
of the error in these guesses in WERR. During bisection, intervals
[left, right] are maintained by storing their mid-points and
semi-widths in the arrays W and WERR respectively.
does bisection to refine the eigenvalues of T,
W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
guesses for these eigenvalues are input in W, the corresponding estimate
of the error in these guesses in WERR. During bisection, intervals
[left, right] are maintained by storing their mid-points and
semi-widths in the arrays W and WERR respectively.
Arguments
| N |
(input) INTEGER
The order of the matrix.
|
| D |
(input) REAL array, dimension (N)
The N diagonal elements of T.
|
| E2 |
(input) REAL array, dimension (N-1)
The Squares of the (N-1) subdiagonal elements of T.
|
| IFIRST |
(input) INTEGER
The index of the first eigenvalue to be computed.
|
| ILAST |
(input) INTEGER
The index of the last eigenvalue to be computed.
|
| RTOL |
(input) REAL
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|). |
| OFFSET |
(input) INTEGER
Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET
through ILAST-OFFSET elements of these arrays are to be used. |
| W |
(input/output) REAL array, dimension (N)
On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
estimates of the eigenvalues of L D L^T indexed IFIRST through ILAST. On output, these estimates are refined. |
| WERR |
(input/output) REAL array, dimension (N)
On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
the errors in the estimates of the corresponding elements in W. On output, these errors are refined. |
| WORK |
(workspace) REAL array, dimension (2*N)
Workspace.
|
| IWORK |
(workspace) INTEGER array, dimension (2*N)
Workspace.
|
| PIVMIN |
(input) REAL
The minimum pivot in the Sturm sequence for T.
|
| SPDIAM |
(input) REAL
The spectral diameter of T.
|
| INFO |
(output) INTEGER
Error flag.
|
Further Details
Based on contributions by
Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
Inderjit Dhillon, University of Texas, Austin, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
Inderjit Dhillon, University of Texas, Austin, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA