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# slicot_sb04qd

### Syntax

 [A_OUT, B_OUT, C_OUT, Z, INFO] = slicot_sb04qd(A_IN, B_IN, C_IN)

### Input argument

A_IN

The leading N-by-N part of this array must contain the coefficient matrix A of the equation.

B_IN

The leading M-by-M part of this array must contain the coefficient matrix B of the equation.

C_IN

The leading N-by-M part of this array must contain the coefficient matrix C of the equation.

### Output argument

A_OUT

The leading N-by-N upper Hessenberg part of this array contains the matrix H, and the remainder of the leading N-by-N part, together with the elements 2,3,...,N of array DWORK, contain the orthogonal transformation matrix U (stored in factored form).

B_OUT

The leading M-by-M part of this array contains the quasi-triangular Schur factor S of the matrix B'.

C_OUT

The leading N-by-M part of this array contains the solution matrix X of the problem.

Z

The leading M-by-M part of this array contains the orthogonal matrix Z used to transform B' to real upper Schur form.

INFO

= 0: successful exit;

### Description

To solve for X the discrete-time Sylvester equation X + AXB = C, where A, B, C and X are general N-by-N, M-by-M, N-by-M and N-by-M matrices respectively. A Hessenberg-Schur method, which reduces A to upper Hessenberg form, H = U'AU, and B' to real Schur form, S = Z'B'Z (with U, Z orthogonal matrices), is used.

SB04QD

### Bibliography

http://slicot.org/objects/software/shared/doc/SB04QD.html

### Example

``````N = 3;
M = 3;
A_IN = [1.0   2.0   3.0;
6.0   7.0   8.0;
9.0   2.0   3.0];
B_IN = [7.0   2.0   3.0;
2.0   1.0   2.0;
3.0   4.0   1.0];
C_IN = [271.0   135.0   147.0;
923.0   494.0   482.0;
578.0   383.0   287.0];

[A_OUT, B_OUT, C_OUT, Z, INFO] = slicot_sb04qd(A_IN, B_IN, C_IN)
```
```

### History

Version Description
1.0.0 initial version

### Author

SLICOT Documentation