CLAIC1 man page on IRIX

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CLAIC1(3F)							    CLAIC1(3F)

NAME
     CLAIC1 - applie one step of incremental condition estimation in its
     simplest version

SYNOPSIS
     SUBROUTINE CLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

	 INTEGER	J, JOB

	 REAL		SEST, SESTPR

	 COMPLEX	C, GAMMA, S

	 COMPLEX	W( J ), X( J )

PURPOSE
     CLAIC1 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 CLAIC1 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] * [ conjg(alpha) ]
					       [ conjg(gamma) ]

     where  alpha =  conjg(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

									Page 1

CLAIC1(3F)							    CLAIC1(3F)

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

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

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

     GAMMA   (input) COMPLEX
	     The diagonal element gamma.

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

     S	     (output) COMPLEX
	     Sine needed in forming xhat.

     C	     (output) COMPLEX
	     Cosine needed in forming xhat.

									Page 2

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