DLAED5 - subroutine computes the I-th eigenvalue of a sym
metric rank-one modification of a 2-by-2 diagonal matrix
diag( D ) + RHO * Z * transpose(Z)
SYNOPSIS
SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
INTEGER I
DOUBLE PRECISION DLAM, RHO
DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
PURPOSE
This subroutine computes the I-th eigenvalue of a symmet
ric rank-one modification of a 2-by-2 diagonal matrix
diag( D ) + RHO * Z * transpose(Z) . The diagonal ele
ments in the array D are assumed to satisfy
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) DOUBLE PRECISION array, dimension (2)
The original eigenvalues. We assume D(1) < D(2).
Z (input) DOUBLE PRECISION array, dimension (2)
The components of the updating vector.
DELTA (output) DOUBLE PRECISION array, dimension (2)
The vector DELTA contains the information necessary
to construct the eigenvectors.
RHO (input) DOUBLE PRECISION
The scalar in the symmetric updating formula.
DLAM (output) DOUBLE PRECISION
The computed lambda_I, the I-th updated eigenvalue.
FURTHER DETAILS
Based on contributions by
Ren-Cang Li, Computer Science Division, University of
California
at Berkeley, USA
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