SLASD5(l)								 )								 SLASD5(l)

NAME

       SLASD5  -  subroutine  computes	the  square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal
       matrix  diag( D ) * diag( D ) + RHO * Z * transpose(Z)

SYNOPSIS

       SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )

	   INTEGER	  I

	   REAL 	  DSIGMA, RHO

	   REAL 	  D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )

PURPOSE

       This subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2  diagonal  matrix
       diag( D ) * diag( D ) + RHO * Z * transpose(Z) .  The diagonal entries in the array D are assumed to satisfy

		  0 <= 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 0 <= D(1) < D(2).

       Z      (input) REAL array, dimension ( 2 )
	      The components of the updating vector.

       DELTA  (output) REAL array, dimension ( 2 )
	      Contains	(D(j)  - lambda_I) in its  j-th component.  The vector DELTA contains the information necessary to construct the eigenvec-
	      tors.

       RHO    (input) REAL
	      The scalar in the symmetric updating formula.

	      DSIGMA (output) REAL The computed lambda_I, the I-th updated eigenvalue.

       WORK   (workspace) REAL array, dimension ( 2 )
	      WORK contains (D(j) + sigma_I) in its  j-th component.

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 							 SLASD5(l)