SLAIC1  - applie one step of incremental condition estima­
       tion in its simplest version


SYNOPSIS

       SUBROUTINE SLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C
                          )

           INTEGER        J, JOB

           REAL           C, GAMMA, S, SEST, SESTPR

           REAL           W( J ), X( J )


PURPOSE

       SLAIC1  applies  one step of incremental condition estima­
       tion in its simplest version: Let x, twonorm(x) = 1, be an
       approximate  singular vector of an j-by-j lower triangular
       matrix L, such that
                twonorm(L*x) = sest
       Then SLAIC1 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 sys­
       tem

           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) REAL array, dimension (J)
               The j-vector x.

               Estimated singular value of j by j matrix L

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

       GAMMA   (input) REAL
               The diagonal element gamma.

       SESTPR  (output) REAL
               Estimated singular value of (j+1) by (j+1)  matrix
               Lhat.

       S       (output) REAL
               Sine needed in forming xhat.

       C       (output) REAL
               Cosine needed in forming xhat.


Man(1) output converted with man2html