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dlarrk.f(3)				      LAPACK				      dlarrk.f(3)

NAME
       dlarrk.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)
	   DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable
	   accuracy.

Function/Subroutine Documentation
   subroutine dlarrk (integerN, integerIW, double precisionGL, double precisionGU, double
       precision, dimension( * )D, double precision, dimension( * )E2, double precisionPIVMIN,
       double precisionRELTOL, double precisionW, double precisionWERR, integerINFO)
       DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

       Purpose:

	    DLARRK computes one eigenvalue of a symmetric tridiagonal
	    matrix T to suitable accuracy. This is an auxiliary code to be
	    called from DSTEMR.

	    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 "Accurate Eigenvalues of a Symmetric Tridiagonal
	    Matrix", Report CS41, Computer Science Dept., Stanford
	    University, July 21, 1966.

       Parameters:
	   N

		     N is INTEGER
		     The order of the tridiagonal matrix T.  N >= 0.

	   IW

		     IW is INTEGER
		     The index of the eigenvalues to be returned.

	   GL

		     GL is DOUBLE PRECISION

	   GU

		     GU is DOUBLE PRECISION
		     An upper and a lower bound on the eigenvalue.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The n diagonal elements of the tridiagonal matrix T.

	   E2

		     E2 is DOUBLE PRECISION array, dimension (N-1)
		     The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

	   PIVMIN

		     PIVMIN is DOUBLE PRECISION
		     The minimum pivot allowed in the Sturm sequence for T.

	   RELTOL

		     RELTOL is DOUBLE PRECISION
		     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.

	   W

		     W is DOUBLE PRECISION

	   WERR

		     WERR is DOUBLE PRECISION
		     The error bound on the corresponding eigenvalue approximation
		     in W.

	   INFO

		     INFO is INTEGER
		     = 0:	Eigenvalue converged
		     = -1:	Eigenvalue did NOT converge

       Internal Parameters:

	     FUDGE   DOUBLE PRECISION, default = 2
		     A "fudge factor" to widen the Gershgorin intervals.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 145 of file dlarrk.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlarrk.f(3)
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