# ?gehbs

Solves a system of interval linear equations by Hansen-Bliek-Rohn procedure.

## Syntax

call sigehbs(trans, n, a, lda, b, ldb, info)

call digehbs(trans, n, a, lda, b, ldb, info)

## Description

The routine ?gehbs uses the Hansen-Bliek-Rohn procedure to compute an enclosure of the solution set to the following interval linear system of equations:

`A*X = B`, if `trans = 'N'`,

`AT*X = B`, if `trans = 'T'` or 'C'.

See “Interval Linear Solvers Code Examples” for example code on using this routine.

## Input Parameters

trans

  CHARACTER(1). Must be one of 'N', 'T', 'C', 'n', 't', or 'c'.

  Indicates the form of the equations system:

  If `trans = 'N'` or 'n', then `A*X = B` is solved for X.

  If `trans = 'T'` or 'C' or 't'or 'c', then `AT*X = B` is solved for X.

n

  INTEGER. The order of A, the number of rows in B (`n ≥ 0`).

a, b

  REAL for sigehbs.

  DOUBLE PRECISION for digehbs.

  Arrays: `a (lda,*)`, `b (ldb,*)`.

  The array a contains the matrix A.

  The array b contains the matrix B, whose columns are the right-hand sides for the systems of equations.

lda

  INTEGER. The first dimension of a, `lda ≥ max(1, n)`.

ldb

  INTEGER. The first dimension of b, `ldb ≥ max(1, n)`.

## Output Parameters

b

  Overwritten by the solution matrix X.

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info ≥ 0`, the execution is not successful.

  If `info = -i`, the i-th parameter has an illegal value.

## Application Notes

If the middle matrix of A is not close to a diagonal matrix, then the midpoint inverse preconditioning by ?gemip routine may be necessary to correct the interval linear system and yield better results.

Parent topic: Routines for Fast Solution of Interval Systems