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Solving the coupled Sylvester-like matrix equations via a new finite iterative algorithm

Masoud Hajarian (Department of Mathematics, Shahid Beheshti University, General Campus, Evin, Tehran, Iran)

Engineering Computations

ISSN: 0264-4401

Article publication date: 3 July 2017

Abstract

Purpose

The purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations.

Design/methodology/approach

In this work, the matrix form of the conjugate direction (CD) algorithm to find the solution X of the coupled Sylvester-like matrix equations:

{A1XB1+M1f1(X)N1=F1,A2XB2+M2f2(X)N2=F2,
with fi(X) = X, fi(X) = X¯, fi(X) = XT and fi(X) = XH for i = 1; 2 has been established.

Findings

It is proven that the algorithm converges to the solution within a finite number of iterations in the absence of round-off errors. Finally, four numerical examples were used to test the proficiency and convergence of the established algorithm.

Originality/value

The numerical examples have led the author to believe that the generalized CD (GCD) algorithm is efficient and it converges more rapidly in comparison with the CGNR and CGNE algorithms.

Keywords

Acknowledgements

The author would like to express his great thankfulness to the referees for valuable comments and suggestions which substantially improved the quality of this paper.

Citation

Hajarian, M. (2017), "Solving the coupled Sylvester-like matrix equations via a new finite iterative algorithm", Engineering Computations, Vol. 34 No. 5, pp. 1446-1467. https://doi.org/10.1108/EC-11-2015-0341

Publisher

:

Emerald Publishing Limited

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