slaed4(3)

NAME

SLAED4 - subroutine computes the I-th updated eigenvalue

of a symmetric rank-one modification to a diagonal matrix whose

elements are given in the array d, and that D(i) < D(j) for i <

j and that RHO > 0

SYNOPSIS

SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
    INTEGER        I, INFO, N
    REAL           DLAM, RHO
    REAL           D( * ), DELTA( * ), Z( * )

PURPOSE

This subroutine computes the I-th updated eigenvalue of a

symmetric rank-one modification to a diagonal matrix whose ele

ments are given in the array d, and that D(i) < D(j) for i < j

and that RHO > 0. This is arranged by the calling routine, and is

no loss in generality. The rank-one modified system is thus

diag( D ) + RHO * Z * Z_transpose.

where we assume the Euclidean norm of Z is 1.

The method consists of approximating the rational func

tions in the secular equation by simpler interpolating rational

functions.

ARGUMENTS

N (input) INTEGER

The length of all arrays.

I (input) INTEGER

The index of the eigenvalue to be computed. 1 <= I

<= N.

D (input) REAL array, dimension (N)

The original eigenvalues. It is assumed that they

are in order, D(I) < D(J) for I < J.

Z (input) REAL array, dimension (N)

The components of the updating vector.

DELTA (output) REAL array, dimension (N)

If N .ne. 1, DELTA contains (D(j) - lambda_I) in

its j-th component. If N = 1, then DELTA(1) = 1. The vector

DELTA contains the information necessary to construct the eigen

vectors.

RHO (input) REAL

The scalar in the symmetric updating formula.

DLAM (output) REAL

The computed lambda_I, the I-th updated eigenvalue.

INFO (output) INTEGER

= 0: successful exit
> 0: if INFO = 1, the updating process failed.

PARAMETERS

Logical variable ORGATI (origin-at-i?) is used for distin

guishing whether D(i) or D(i+1) is treated as the origin.

ORGATI = .true. origin at i ORGATI = .false. origin

at i+1

Logical variable SWTCH3 (switch-for-3-poles?) is for not

ing if we are working with THREE poles!

MAXIT is the maximum number of iterations allowed for each

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

SLAED4(3)