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

Solving the coupled Sylvester-like matrix equations via a new finite iterative algorithm PurposeThe purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations.Design/methodology/approachIn 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.FindingsIt 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/valueThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

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

Hajarian, Masoud
Engineering Computations , Volume 34 (5): 22 – Jul 3, 2017
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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0264-4401
DOI
10.1108/EC-11-2015-0341
Publisher site
See Article on Publisher Site

Abstract

PurposeThe purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations.Design/methodology/approachIn 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.FindingsIt 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/valueThe 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.

Journal

Engineering Computations – Emerald Publishing

Published: Jul 3, 2017

References

  • The matrix equation AX¯ − XB = C and its special cases
  • Consimilarity and the matrix equation AX¯ − XB = C
  • Pole assignment via Sylvester’s equation
  • On the solution of the linear matrix equation X = Af(X)B + C
  • A novel numerical method for exact model matching problem with stability
  • Iterative algorithms for the generalized centro-symmetric and central anti-symmetric solutions of general coupled matrix
  • Construction of an iterative method for solving generalized coupled Sylvester matrix equations
  • Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems