---
name: "dlarrk"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlarrk/3lapack"
---

# dlarrk(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE DLARRK(

  N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)

- IMPLICIT

  NONE

- INTEGER

  INFO, IW, N

- DOUBLE

  PRECISION PIVMIN, RELTOL, GL, GU, W, WERR

- DOUBLE

  PRECISION D( \* ), E2( \* )

## 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.\

## ARGUMENTS

- N (input) INTEGER

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

- IW (input) INTEGER

  The index of the eigenvalues to be returned.

- GL (input) DOUBLE PRECISION

  GU      (input) DOUBLE PRECISION An upper and a lower bound on the eigenvalue.

- D (input) DOUBLE PRECISION array, dimension (N)

  The n diagonal elements of the tridiagonal matrix T.

- E2 (input) DOUBLE PRECISION array, dimension (N-1)

  The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

- PIVMIN (input) DOUBLE PRECISION

  The minimum pivot allowed in the Sturm sequence for T.

- RELTOL (input) 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 (output) DOUBLE PRECISION

  - WERR (output) DOUBLE PRECISION

  The error bound on the corresponding eigenvalue approximation in W.

- INFO (output) INTEGER

  \= 0:       Eigenvalue converged\
   \= -1:      Eigenvalue did NOT converge

## PARAMETERS

- FUDGE DOUBLE PRECISION, default = 2

  A "fudge factor" to widen the Gershgorin intervals.