slarrb(3)

NAME

SLARRB - the relatively robust representation(RRR) L D

L^T, SLARRB does ``limited'' bisection to locate the eigenvalues

of L D L^T,

SYNOPSIS

SUBROUTINE SLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA,
RELTOL, W, WGAP, WERR, WORK, IWORK, INFO )
    INTEGER        IFIRST, ILAST, INFO, N
    REAL           RELTOL, SIGMA
    INTEGER        IWORK( * )
    REAL           D( * ), L( * ), LD( * ), LLD( * ), W( *
), WERR( * ), WGAP( * ), WORK( * )

PURPOSE

Given the relatively robust representation(RRR) L D L^T,

SLARRB does ``limited'' bisection to locate the eigenvalues of L

D L^T, W( IFIRST ) thru' W( ILAST ), to more accuracy. Intervals

[left, right] are maintained by storing their mid-points and se

mi-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 the diagonal matrix D.

L (input) REAL array, dimension (N-1)

The n-1 subdiagonal elements of the unit bidiago

nal matrix L.

LD (input) REAL array, dimension (N-1)

The n-1 elements L(i)*D(i).

LLD (input) REAL array, dimension (N-1)

The n-1 elements L(i)*L(i)*D(i).

IFIRST (input) INTEGER

The index of the first eigenvalue in the cluster.

ILAST (input) INTEGER

The index of the last eigenvalue in the cluster.

SIGMA (input) REAL

The shift used to form L D L^T (see SLARRF).

RELTOL (input) REAL

The relative tolerance.

W (input/output) REAL array, dimension (N)

On input, W( IFIRST ) thru' W( ILAST ) are esti

mates of the corresponding eigenvalues of L D L^T. On output,

these estimates are ``refined''.

WGAP (input/output) REAL array, dimension (N)

The gaps between the eigenvalues of L D L^T. Very

small gaps are changed on output.

WERR (input/output) REAL array, dimension (N)

On input, WERR( IFIRST ) thru' WERR( ILAST ) are

the errors in the estimates W( IFIRST ) thru' W( ILAST ). On

output, these are the ``refined'' errors.

WORK (input) REAL array, dimension (???)

Workspace.

IWORK (input) INTEGER array, dimension (2*N)

Workspace.

INFO (output) INTEGER

Error flag.

FURTHER DETAILS

Based on contributions by

Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0 15 June 2000

SLARRB(3)