DLAIC1(l)								 )								 DLAIC1(l)

NAME

       DLAIC1 - applie one step of incremental condition estimation in its simplest version

SYNOPSIS

       SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

	   INTEGER	  J, JOB

	   DOUBLE	  PRECISION C, GAMMA, S, SEST, SESTPR

	   DOUBLE	  PRECISION W( J ), X( J )

PURPOSE

       DLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vec-
       tor of an j-by-j lower triangular matrix L, such that
		twonorm(L*x) = sest
       Then DLAIC1 computes sestpr, s, c such that
       the vector
		       [ s*x ]
		xhat = [  c  ]
       is an approximate singular vector of
		       [ L     0  ]
		Lhat = [ w' gamma ]
       in the sense that
		twonorm(Lhat*xhat) = sestpr.

       Depending on JOB, an estimate for the largest or smallest singular value is computed.

       Note that [s c]' and sestpr**2 is an eigenpair of the system

	   diag(sest*sest, 0) + [alpha	gamma] * [ alpha ]
						 [ gamma ]

       where  alpha =  x'*w.

ARGUMENTS

       JOB     (input) INTEGER
	       = 1: an estimate for the largest singular value is computed.
	       = 2: an estimate for the smallest singular value is computed.

       J       (input) INTEGER
	       Length of X and W

       X       (input) DOUBLE PRECISION array, dimension (J)
	       The j-vector x.

       SEST    (input) DOUBLE PRECISION
	       Estimated singular value of j by j matrix L

       W       (input) DOUBLE PRECISION array, dimension (J)
	       The j-vector w.

       GAMMA   (input) DOUBLE PRECISION
	       The diagonal element gamma.

       SEDTPR  (output) DOUBLE PRECISION
	       Estimated singular value of (j+1) by (j+1) matrix Lhat.

       S       (output) DOUBLE PRECISION
	       Sine needed in forming xhat.

       C       (output) DOUBLE PRECISION
	       Cosine needed in forming xhat.

LAPACK version 3.0						   15 June 2000 							 DLAIC1(l)