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

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