Solving the coupled Sylvester-like matrix equations via a new finite iterative algorithm. Issue 5 (3rd July 2017) - Hajarian, Masoud
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: A 1 X B 1 + M 1 f 1 ( X ) N 1 = F 1, A 2 X B 2 + M 2 f 2 ( X ) N 2 = F 2, with fi ( X ) = X, fi ( X ) = X ¯, fi ( X ) = X T and fi ( 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.,