dlarrk-f(3)

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 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.

Date:

September 2012

Definition at line 145 of file dlarrk.f.

Author

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