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## dlarrk()

subroutine dlarrk | ( | integer | n,
|  | integer | iw,
|  | double precision | gl,
|  | double precision | gu,
|  | double precision, dimension( * ) | d,
|  | double precision, dimension( * ) | e2,
|  | double precision | pivmin,
|  | double precision | reltol,
|  | double precision | w,
|  | double precision | werr,
|  | integer | info )

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

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

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 , 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 DOUBLE PRECISION
      !>

  [in]

  GU

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

  [in]

  D

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

  [in]

  E2

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

  [in]

  PIVMIN

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

  [in]

  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.
      !>

  [out]

  W

      !>          W is DOUBLE PRECISION
      !>

  [out]

  WERR

      !>          WERR is DOUBLE PRECISION
      !>          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   DOUBLE PRECISION, default = 2
      !>          A  to widen the Gershgorin intervals.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.