ZLAIC1(3F)							    ZLAIC1(3F)

NAME    [Toc]    [Back]

     ZLAIC1 - applie one step of incremental condition estimation in its
     simplest version

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	ZLAIC1(	JOB, J,	X, SEST, W, GAMMA, SESTPR, S, C	)

	 INTEGER	J, JOB

	 DOUBLE		PRECISION SEST,	SESTPR

	 COMPLEX*16	C, GAMMA, S

	 COMPLEX*16	W( J ),	X( J )

PURPOSE    [Toc]    [Back]

     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' 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    [Toc]    [Back]

     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





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ZLAIC1(3F)							    ZLAIC1(3F)



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

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

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

     GAMMA   (input) COMPLEX*16
	     The diagonal element gamma.

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

     S	     (output) COMPLEX*16
	     Sine needed in forming xhat.

     C	     (output) COMPLEX*16
	     Cosine needed in forming xhat.
ZLAIC1(3F)							    ZLAIC1(3F)

NAME    [Toc]    [Back]

     ZLAIC1 - applie one step of incremental condition estimation in its
     simplest version

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	ZLAIC1(	JOB, J,	X, SEST, W, GAMMA, SESTPR, S, C	)

	 INTEGER	J, JOB

	 DOUBLE		PRECISION SEST,	SESTPR

	 COMPLEX*16	C, GAMMA, S

	 COMPLEX*16	W( J ),	X( J )

PURPOSE    [Toc]    [Back]

     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' 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    [Toc]    [Back]

     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






ZLAIC1(3F)							    ZLAIC1(3F)



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

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

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

     GAMMA   (input) COMPLEX*16
	     The diagonal element gamma.

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

     S	     (output) COMPLEX*16
	     Sine needed in forming xhat.

     C	     (output) COMPLEX*16
	     Cosine needed in forming xhat.


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