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.TH DLASD5 l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
DLASD5 - 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)
.SH SYNOPSIS
.TP 19
SUBROUTINE DLASD5(
I, D, Z, DELTA, RHO, DSIGMA, WORK )
.TP 19
.ti +4
INTEGER
I
.TP 19
.ti +4
DOUBLE
PRECISION DSIGMA, RHO
.TP 19
.ti +4
DOUBLE
PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
.SH 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 .
.br
We also assume RHO > 0 and that the Euclidean norm of the vector
Z is one.
.br
.SH ARGUMENTS
.TP 7
I (input) INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
.TP 7
D (input) DOUBLE PRECISION array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) < D(2).
.TP 7
Z (input) DOUBLE PRECISION array, dimension ( 2 )
The components of the updating vector.
.TP 7
DELTA (output) DOUBLE PRECISION array, dimension ( 2 )
Contains (D(j) - lambda_I) in its j-th component.
The vector DELTA contains the information necessary
to construct the eigenvectors.
.TP 7
RHO (input) DOUBLE PRECISION
The scalar in the symmetric updating formula.
DSIGMA (output) DOUBLE PRECISION
The computed lambda_I, the I-th updated eigenvalue.
.TP 7
WORK (workspace) DOUBLE PRECISION array, dimension ( 2 )
WORK contains (D(j) + sigma_I) in its j-th component.
.SH FURTHER DETAILS
Based on contributions by
.br
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA
.br
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