 DLARRJ(3) the initial eigenvalue approximations of T, DLARRJ does bisection to refine the eigenvalues of T,

## SYNOPSIS

SUBROUTINE DLARRJ(
N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO )

INTEGER IFIRST, ILAST, INFO, N, OFFSET

DOUBLE PRECISION PIVMIN, RTOL, SPDIAM

INTEGER IWORK( * )

DOUBLE PRECISION D( * ), E2( * ), W( * ), WERR( * ), WORK( * )

## PURPOSE

Given the initial eigenvalue approximations of T, DLARRJ 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) DOUBLE PRECISION array, dimension (N)
The N diagonal elements of T.
E2 (input) DOUBLE PRECISION 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) DOUBLE PRECISION
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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2*N)
Workspace.
IWORK (workspace) INTEGER array, dimension (2*N)
Workspace.
PIVMIN (input) DOUBLE PRECISION
The minimum pivot in the Sturm sequence for T.
SPDIAM (input) DOUBLE PRECISION
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