LAPACK

NAME¶

larrk - larrk: step in stemr, compute one eigval

SYNOPSIS¶

Functions¶

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. subroutine slarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

Detailed Description¶

Function Documentation¶

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.

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 is INTEGER


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



          IW is INTEGER


          The index of the eigenvalues to be returned.



          GL is DOUBLE PRECISION



          GU is DOUBLE PRECISION


          An upper and a lower bound on the eigenvalue.



          D is DOUBLE PRECISION array, dimension (N)


          The n diagonal elements of the tridiagonal matrix T.



          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 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.

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.