dlarrf(3)

NAME

DLARRF - the initial representation L D L^T and its clus

ter of close eigenvalues (in a relative measure), W( IFIRST ), W(

IFIRST+1 ), ..

SYNOPSIS

SUBROUTINE DLARRF( N, D, L, LD,  LLD,  IFIRST,  ILAST,  W,
DPLUS, LPLUS, WORK, IWORK, INFO )
    INTEGER        IFIRST, ILAST, INFO, N
    INTEGER        IWORK( * )
    DOUBLE          PRECISION  D( * ), DPLUS( * ), L( * ),
LD( * ), LLD( * ), LPLUS( * ), W( * ), WORK( * )

PURPOSE

Given the initial representation L D L^T and its cluster

of close eigenvalues (in a relative measure), W( IFIRST ), W(

IFIRST+1 ), ... W( ILAST ), DLARRF finds a new relatively robust

representation L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at

least one of the eigenvalues of L(+) D(+) L(+)^T is relatively

isolated.

ARGUMENTS

N (input) INTEGER

The order of the matrix.

D (input) DOUBLE PRECISION array, dimension (N)

The n diagonal elements of the diagonal matrix D.

L (input) DOUBLE PRECISION array, dimension (N-1)

The (n-1) subdiagonal elements of the unit bidiag

onal matrix L.

LD (input) DOUBLE PRECISION array, dimension (N-1)

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

LLD (input) DOUBLE PRECISION 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.

W (input/output) DOUBLE PRECISION array, dimension

(N)

On input, the eigenvalues of L D L^T in ascending

order. W( IFIRST ) through W( ILAST ) form the cluster of rela

tively close eigenalues. On output, W( IFIRST ) thru' W( ILAST )

are estimates of the corresponding eigenvalues of L(+) D(+)

L(+)^T.

SIGMA (input) DOUBLE PRECISION

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

DPLUS (output) DOUBLE PRECISION array, dimension (N)

The n diagonal elements of the diagonal matrix

D(+).

LPLUS (output) DOUBLE PRECISION array, dimension (N)

The first (n-1) elements of LPLUS contain the sub

diagonal elements of the unit bidiagonal matrix L(+). LPLUS( N )

is set to SIGMA.

WORK (input) DOUBLE PRECISION array, dimension (???)

Workspace.

FURTHER DETAILS

Based on contributions by

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

LAPACK version 3.0 15 June 2000

DLARRF(3)