## SB04NY

### Solving a system of equations in Hessenberg form with one offdiagonal and one right-hand side

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

Purpose

```  To solve a system of equations in Hessenberg form with one
offdiagonal and one right-hand side.

```
Specification
```      SUBROUTINE SB04NY( RC, UL, M, A, LDA, LAMBDA, D, TOL, IWORK,
\$                   DWORK, LDDWOR, INFO )
C     .. Scalar Arguments ..
CHARACTER         RC, UL
INTEGER           INFO, LDA, LDDWOR, M
DOUBLE PRECISION  LAMBDA, TOL
C     .. Array Arguments ..
INTEGER           IWORK(*)
DOUBLE PRECISION  A(LDA,*), D(*), DWORK(LDDWOR,*)

```
Arguments

Mode Parameters

```  RC      CHARACTER*1
Indicates processing by columns or rows, as follows:
= 'R':  Row transformations are applied;
= 'C':  Column transformations are applied.

UL      CHARACTER*1
Indicates whether AB is upper or lower Hessenberg matrix,
as follows:
= 'U':  AB is upper Hessenberg;
= 'L':  AB is lower Hessenberg.

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

A       (input) DOUBLE PRECISION array, dimension (LDA,M)
The leading M-by-M part of this array must contain a
matrix A in Hessenberg form.

LDA     INTEGER
The leading dimension of array A.  LDA >= MAX(1,M).

LAMBDA  (input) DOUBLE PRECISION
This variable must contain the value to be added to the
diagonal elements of A.

D       (input/output) DOUBLE PRECISION array, dimension (M)
On entry, this array must contain the right-hand side
vector of the Hessenberg system.
On exit, if INFO = 0, this array contains the solution
vector of the Hessenberg system.

```
Tolerances
```  TOL     DOUBLE PRECISION
The tolerance to be used to test for near singularity of
the triangular factor R of the Hessenberg matrix. A matrix
whose estimated condition number is less than 1/TOL is
considered to be nonsingular.

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

DWORK   DOUBLE PRECISION array, dimension (LDDWOR,M+3)
The leading M-by-M part of this array is used for
computing the triangular factor of the QR decomposition
of the Hessenberg matrix. The remaining 3*M elements are
used as workspace for the computation of the reciprocal
condition estimate.

LDDWOR  INTEGER
The leading dimension of array DWORK.  LDDWOR >= MAX(1,M).

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
= 1:  if the Hessenberg matrix is (numerically) singular.
That is, its estimated reciprocal condition number
is less than or equal to TOL.

```
Numerical Aspects
```  None.

```
```  None
```
Example

Program Text

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