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RedHat 9 (Linux i386) - man page for slarrb (redhat section l)

SLARRB(l)					)					SLARRB(l)

NAME
       SLARRB - the relatively robust representation(RRR) L D L^T, SLARRB does ``limited'' bisec-
       tion to locate the eigenvalues of L D L^T,

SYNOPSIS
       SUBROUTINE SLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL, W,  WGAP,  WERR,  WORK,
			  IWORK, INFO )

	   INTEGER	  IFIRST, ILAST, INFO, N

	   REAL 	  RELTOL, SIGMA

	   INTEGER	  IWORK( * )

	   REAL 	  D(  * ), L( * ), LD( * ), LLD( * ), W( * ), WERR( * ), WGAP( * ), WORK(
			  * )

PURPOSE
       Given the relatively robust representation(RRR) L D L^T, SLARRB does ``limited'' bisection
       to  locate  the	eigenvalues  of  L D L^T, W( IFIRST ) thru' W( ILAST ), to more accuracy.
       Intervals [left, right] are maintained by storing their mid-points and semi-widths in  the
       arrays W and WERR respectively.

ARGUMENTS
       N       (input) INTEGER
	       The order of the matrix.

       D       (input) REAL array, dimension (N)
	       The n diagonal elements of the diagonal matrix D.

       L       (input) REAL array, dimension (N-1)
	       The n-1 subdiagonal elements of the unit bidiagonal matrix L.

       LD      (input) REAL array, dimension (N-1)
	       The n-1 elements L(i)*D(i).

       LLD     (input) REAL array, dimension (N-1)
	       The n-1 elements L(i)*L(i)*D(i).

       IFIRST  (input) INTEGER
	       The index of the first eigenvalue in the cluster.

       ILAST   (input) INTEGER
	       The index of the last eigenvalue in the cluster.

       SIGMA   (input) REAL
	       The shift used to form L D L^T (see SLARRF).

       RELTOL  (input) REAL
	       The relative tolerance.

       W       (input/output) REAL array, dimension (N)
	       On  input,  W( IFIRST ) thru' W( ILAST ) are estimates of the corresponding eigen-
	       values of L D L^T.  On output, these estimates are ``refined''.

       WGAP    (input/output) REAL array, dimension (N)
	       The gaps between the eigenvalues of L D L^T. Very small gaps are changed  on  out-
	       put.

       WERR    (input/output) REAL array, dimension (N)
	       On  input,  WERR(  IFIRST ) thru' WERR( ILAST ) are the errors in the estimates W(
	       IFIRST ) thru' W( ILAST ).  On output, these are the ``refined'' errors.

       WORK    (input) REAL array, dimension (???)
	       Workspace.

       IWORK   (input) INTEGER array, dimension (2*N)
	       Workspace.

       INFO    (output) INTEGER
	       Error flag.

FURTHER DETAILS
       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0			   15 June 2000 				SLARRB(l)


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