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

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 f_i(X) = X, f_i(X) = X¯, f_i(X) = X^T and f_i(X) = X^H 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.

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