slaed9(3)

NAME

SLAED9 - find the roots of the secular equation, as de

fined by the values in D, Z, and RHO, between KSTART and KSTOP

SYNOPSIS

SUBROUTINE  SLAED9(  K,  KSTART, KSTOP, N, D, Q, LDQ, RHO,
DLAMDA, W, S, LDS, INFO )
    INTEGER        INFO, K, KSTART, KSTOP, LDQ, LDS, N
    REAL           RHO
    REAL           D( * ), DLAMDA( * ), Q( LDQ,  *  ),  S(
LDS, * ), W( * )

PURPOSE

SLAED9 finds the roots of the secular equation, as defined

by the values in D, Z, and RHO, between KSTART and KSTOP. It

makes the appropriate calls to SLAED4 and then stores the new ma

trix of eigenvectors for use in calculating the next level of Z

vectors.

ARGUMENTS

K (input) INTEGER

The number of terms in the rational function to be

solved by SLAED4. K >= 0.

KSTART (input) INTEGER

KSTOP (input) INTEGER The updated eigenvalues

Lambda(I), KSTART <= I <= KSTOP are to be computed. 1 <= KSTART

<= KSTOP <= K.

N (input) INTEGER

The number of rows and columns in the Q matrix. N

>= K (delation may result in N > K).

D (output) REAL array, dimension (N)

D(I) contains the updated eigenvalues for KSTART

<= I <= KSTOP.

Q (workspace) REAL array, dimension (LDQ,N)

LDQ (input) INTEGER

The leading dimension of the array Q. LDQ >= max(

1, N ).

RHO (input) REAL

The value of the parameter in the rank one update

equation. RHO >= 0 required.

DLAMDA (input) REAL array, dimension (K)

The first K elements of this array contain the old

roots of the deflated updating problem. These are the poles of

the secular equation.

W (input) REAL array, dimension (K)

The first K elements of this array contain the

components of the deflation-adjusted updating vector.

S (output) REAL array, dimension (LDS, K)

Will contain the eigenvectors of the repaired ma

trix which will be stored for subsequent Z vector calculation and

multiplied by the previously accumulated eigenvectors to update

the system.

LDS (input) INTEGER

The leading dimension of S. LDS >= max( 1, K ).

INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille

gal value.
> 0: if INFO = 1, an eigenvalue did not converge

FURTHER DETAILS

Based on contributions by

Jeff Rutter, Computer Science Division, University of

California
at Berkeley, USA

LAPACK version 3.0 15 June 2000

SLAED9(3)