## MB02TD

### Estimation of the reciprocal condition number of an upper Hessenberg matrix

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To estimate the reciprocal of the condition number of an upper
Hessenberg matrix H, in either the 1-norm or the infinity-norm,
using the LU factorization computed by MB02SD.

```
Specification
```      SUBROUTINE MB02TD( NORM, N, HNORM, H, LDH, IPIV, RCOND, IWORK,
\$                   DWORK, INFO )
C     .. Scalar Arguments ..
CHARACTER          NORM
INTEGER            INFO, LDH, N
DOUBLE PRECISION   HNORM, RCOND
C     .. Array Arguments ..
INTEGER            IPIV( * ), IWORK( * )
DOUBLE PRECISION   DWORK( * ), H( LDH, * )

```
Arguments

Mode Parameters

```  NORM    CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.

```
Input/Output Parameters
```  N       (input) INTEGER
The order of the matrix H.  N >= 0.

HNORM   (input) DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix H.
If NORM = 'I', the infinity-norm of the original matrix H.

H       (input) DOUBLE PRECISION array, dimension (LDH,N)
The factors L and U from the factorization H = P*L*U
as computed by MB02SD.

LDH     INTEGER
The leading dimension of the array H.  LDH >= max(1,N).

IPIV    (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix
was interchanged with row IPIV(i).

RCOND   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix H,
computed as RCOND = 1/(norm(H) * norm(inv(H))).

```
Workspace
```  IWORK   INTEGER array, dimension (N)

DWORK   DOUBLE PRECISION array, dimension (3*N)

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value.

```
Method
```  An estimate is obtained for norm(inv(H)), and the reciprocal of
the condition number is computed as
RCOND = 1 / ( norm(H) * norm(inv(H)) ).

```
References
```  -

```
Numerical Aspects
```                             2
The algorithm requires 0( N ) operations.

```
```  None
```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```