NAME¶

SLAED5 - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j

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 symmetric rank-one modification of a 2-by-2 diagonal matrix 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