slaed5(3)

NAME

SLAED5 - 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 SLAED5( I, D, Z, DELTA, RHO, DLAM )
    INTEGER        I
    REAL           DLAM, RHO
    REAL           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 elements 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) REAL array, dimension (2)

The original eigenvalues. We assume D(1) < D(2).

Z (input) REAL array, dimension (2)

The components of the updating vector.

DELTA (output) REAL array, dimension (2)

The vector DELTA contains the information necessary

to construct the eigenvectors.

RHO (input) REAL

The scalar in the symmetric updating formula.

DLAM (output) REAL

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

LAPACK version 3.0 15 June 2000

SLAED5(3)