slarrk()

subroutine slarrk	(	integer	n,
		integer	iw,
		real	gl,
		real	gu,
		real, dimension( * )	d,
		real, dimension( * )	e2,
		real	pivmin,
		real	reltol,
		real	w,
		real	werr,
		integer	info )

SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

Download SLARRK + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> SLARRK computes one eigenvalue of a symmetric tridiagonal
!> matrix T to suitable accuracy. This is an auxiliary code to be
!> called from SSTEMR.
!>
!> To avoid overflow, the matrix must be scaled so that its
!> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
!> accuracy, it should not be much smaller than that.
!>
!> See W. Kahan , Report CS41, Computer Science Dept., Stanford
!> University, July 21, 1966.
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the tridiagonal matrix T. N >= 0. !>
[in]	IW	!> IW is INTEGER !> The index of the eigenvalues to be returned. !>
[in]	GL	!> GL is REAL !>
[in]	GU	!> GU is REAL !> An upper and a lower bound on the eigenvalue. !>
[in]	D	!> D is REAL array, dimension (N) !> The n diagonal elements of the tridiagonal matrix T. !>
[in]	E2	!> E2 is REAL array, dimension (N-1) !> The (n-1) squared off-diagonal elements of the tridiagonal matrix T. !>
[in]	PIVMIN	!> PIVMIN is REAL !> The minimum pivot allowed in the Sturm sequence for T. !>
[in]	RELTOL	!> RELTOL is REAL !> The minimum relative width of an interval. When an interval !> is narrower than RELTOL times the larger (in !> magnitude) endpoint, then it is considered to be !> sufficiently small, i.e., converged. Note: this should !> always be at least radix*machine epsilon. !>
[out]	W	!> W is REAL !>
[out]	WERR	!> WERR is REAL !> The error bound on the corresponding eigenvalue approximation !> in W. !>
[out]	INFO	!> INFO is INTEGER !> = 0: Eigenvalue converged !> = -1: Eigenvalue did NOT converge !>

Internal Parameters:

!>  FUDGE   REAL            , default = 2
!>          A  to widen the Gershgorin intervals.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.