dlarrk.f (3) Linux Manual Page

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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