# ?gekws

Solves a system of interval linear equations by Krawczyk iteration method.

## Syntax

call sigekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

call digekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

call crgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

call zrgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

call ccgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

call zcgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

## Description

The routine ?gekws uses the Krawczyk interval iteration 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'`

`AH*X = B`, if `trans =` 'C' (for complex matrices only).

## 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 't', then `AT*X = B` is solved for X.

  If `trans =` 'C' or 'c', then `AH*X = B` is solved for X.

n

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

nrhs

  INTEGER. The number of right-hand sides (`nrhs ≥ 0`).

a, b

  S_INTERVAL for sigekws.

  D_INTERVAL for digekws.

  CR_INTERVAL for crgekws.

  ZR_INTERVAL for zrgekws.

  CC_INTERVAL for ccgekws.

  ZC_INTERVAL for zcgekws.

  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)`.

epsilon

  REAL for sigekws, crgekws, and ccgekws.

  DOUBLE PRECISION for digekws, zrgekws, and zcgekws.

  The prescribed accuracy of the estimate.

## Output Parameters

b

  Overwritten by an enclosure of 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

Krawczyk interval iteration already incorporates midpoint inverse preconditioning, so that additional application of ?gemip routines is not necessary and does not improve the overall efficiency.

Parent topic: Routines for Fast Solution of Interval Systems