ZLAIC1 applies one step of incremental condition estimation 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 ZLAIC1 computes sestpr, s, c such that
 the vector
                 [ s*x ]
          xhat = [  c  ]
 is an approximate singular vector of
                 [ L       0  ]
          Lhat = [ w**H 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]**H and sestpr**2 is an eigenpair of the system
     diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
                                           [ conjg(gamma) ]
 where  alpha =  x**H * w.

JOB

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

J

          J is INTEGER
          Length of X and W

X

          X is COMPLEX*16 array, dimension (J)
          The j-vector x.

SEST

          SEST is DOUBLE PRECISION
          Estimated singular value of j by j matrix L

W

          W is COMPLEX*16 array, dimension (J)
          The j-vector w.

GAMMA

          GAMMA is COMPLEX*16
          The diagonal element gamma.

SESTPR

          SESTPR is DOUBLE PRECISION
          Estimated singular value of (j+1) by (j+1) matrix Lhat.

S

          S is COMPLEX*16
          Sine needed in forming xhat.

C

          C is COMPLEX*16
          Cosine needed in forming xhat.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.