# dlarrk.f man page

dlarrk.f —

## Synopsis

### Functions/Subroutines

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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dlarrk(3) is an alias of dlarrk.f(3).