dlarrj()

subroutine dlarrj	(	integer	n,
		double precision, dimension( * )	d,
		double precision, dimension( * )	e2,
		integer	ifirst,
		integer	ilast,
		double precision	rtol,
		integer	offset,
		double precision, dimension( * )	w,
		double precision, dimension( * )	werr,
		double precision, dimension( * )	work,
		integer, dimension( * )	iwork,
		double precision	pivmin,
		double precision	spdiam,
		integer	info )

DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

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Purpose:

!>
!> Given the initial eigenvalue approximations of T, DLARRJ
!> does  bisection to refine the eigenvalues of T,
!> W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
!> guesses for these eigenvalues are input in W, the corresponding estimate
!> of the error in these guesses in WERR. During bisection, intervals
!> [left, right] are maintained by storing their mid-points and
!> semi-widths in the arrays W and WERR respectively.
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the matrix. !>
[in]	D	!> D is DOUBLE PRECISION array, dimension (N) !> The N diagonal elements of T. !>
[in]	E2	!> E2 is DOUBLE PRECISION array, dimension (N-1) !> The Squares of the (N-1) subdiagonal elements of T. !>
[in]	IFIRST	!> IFIRST is INTEGER !> The index of the first eigenvalue to be computed. !>
[in]	ILAST	!> ILAST is INTEGER !> The index of the last eigenvalue to be computed. !>
[in]	RTOL	!> RTOL is DOUBLE PRECISION !> Tolerance for the convergence of the bisection intervals. !> An interval [LEFT,RIGHT] has converged if !> RIGHT-LEFT < RTOL*MAX(|LEFT|,|RIGHT|). !>
[in]	OFFSET	!> OFFSET is INTEGER !> Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET !> through ILAST-OFFSET elements of these arrays are to be used. !>
[in,out]	W	!> W is DOUBLE PRECISION array, dimension (N) !> On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are !> estimates of the eigenvalues of L D L^T indexed IFIRST through !> ILAST. !> On output, these estimates are refined. !>
[in,out]	WERR	!> WERR is DOUBLE PRECISION array, dimension (N) !> On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are !> the errors in the estimates of the corresponding elements in W. !> On output, these errors are refined. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (2*N) !> Workspace. !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (2*N) !> Workspace. !>
[in]	PIVMIN	!> PIVMIN is DOUBLE PRECISION !> The minimum pivot in the Sturm sequence for T. !>
[in]	SPDIAM	!> SPDIAM is DOUBLE PRECISION !> The spectral diameter of T. !>
[out]	INFO	!> INFO is INTEGER !> Error flag. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
Inderjit Dhillon, University of Texas, Austin, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA