SLASD5 - subroutine computes the square root of the I-th
eigenvalue of a positive symmetric rank-one modification
of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO *
Z * transpose(Z)
SYNOPSIS
SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
INTEGER I
REAL DSIGMA, RHO
REAL D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
PURPOSE
This subroutine computes the square root of the I-th
eigenvalue of a positive symmetric rank-one modification
of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO *
Z * transpose(Z) . The diagonal entries in the array D
are assumed to satisfy
0 <= D(i) < D(j) for i < j .
We also assume RHO > 0 and that the Euclidean norm of the
vector Z is one.
ARGUMENTS
I (input) INTEGER
The index of the eigenvalue to be computed. I = 1
or I = 2.
D (input) REAL array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) <
D(2).
Z (input) REAL array, dimension ( 2 )
The components of the updating vector.
DELTA (output) REAL array, dimension ( 2 )
Contains (D(j) - lambda_I) in its j-th component.
The vector DELTA contains the information necessary
to construct the eigenvectors.
RHO (input) REAL
The scalar in the symmetric updating formula.
DSIGMA (output) REAL The computed lambda_I, the I-
th updated eigenvalue.
WORK (workspace) REAL array, dimension ( 2 )
WORK contains (D(j) + sigma_I) in its j-th compo
nent.
Based on contributions by
Ren-Cang Li, Computer Science Division, University of
California
at Berkeley, USA
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