Publication Cover
Automatika
Journal for Control, Measurement, Electronics, Computing and Communications
Volume 65, 2024 - Issue 3
143
Views
0
CrossRef citations to date
0
Altmetric
Research Article

The relaxed gradient based iterative algorithm for solving the generalized coupled complex conjugate and transpose Sylvester matrix equations

, , &
Pages 1241-1258 | Received 18 Jul 2023, Accepted 21 May 2024, Published online: 05 Jun 2024

References

  • Hajarian M. Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm. Comput Math Appl. 2018;76:686–700. doi: 10.1016/j.camwa.2018.05.010
  • Hajarian M. Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations. Comput Appl Math. 2015;34:755–771. doi: 10.1007/s40314-014-0138-7
  • Zhou Y-H, Zhang X, Ding F. Partially-coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models. Appl Math Comput. 2022;414:Article ID 126663.
  • Dehghan M, Hajarian M. The generalised Sylvester matrix equations over the generalized bisymmetric and skew-symmetric matrices. Int J Syst Sci. 2012;43:1580–1590. doi: 10.1080/00207721.2010.549584
  • Zhou B, Wei X-Z, Duan G-R. Stability and stabilization of discrete-time periodic linear systems with actuator saturation. Automatica. 2011;47:1813–1820. doi: 10.1016/j.automatica.2011.04.015
  • Zhou B, Duan G-R. Periodic Lyapunov equation based approaches to the stabilization of continuous-time periodic linear systems. IEEE Trans Automat Contr. 2011;57:2139–2146. doi: 10.1109/TAC.2011.2181796
  • Ding F, Wang F. Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering. J Franklin Inst. 2017;354:1321–1339. doi: 10.1016/j.jfranklin.2016.11.030
  • Shen H-L, Peng C, Zhang T. Gradient based iterative solutions for Sylvester conjugate matrix equations. J Math Res Appl. 2017;03:103–118.
  • Li X, Ding J, Ding F. Gradient based iterative solutions for general linear matrix equations. Comput Math Appl. 2009;58:1441–1448. doi: 10.1016/j.camwa.2009.06.047
  • Li X, Liu Y-J, Yang H-Z. Gradient based and least squares based iterative algorithms for matrix equations AXB+CXTD=F. Appl Math Comput. 2010;217:2191–2199.
  • Bai Z-Z, Guo X-X, Yin J-F. On two iteration methods for the quadratic matrix equations. Int J Numer Anal Model. 2005;2:114–122.
  • Chen Z-B, Chen X-S. Modification on the convergence results of the Sylvester matrix equation AX + XB = C. J Franklin Inst. 2022;359:3126–3147. doi: 10.1016/j.jfranklin.2022.02.021
  • Xu L, Ding F, Zhu Q-M. Separable synchronous multi-innovation gradient-based iterative signal modeling from on-line measurements. IEEE Trans Instrum Meas. 2022;71:1–13.
  • Ding F. Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data. J Comput Appl Math. 2023;426:Article ID 115107. doi: 10.1016/j.cam.2023.115107
  • Ding J, Liu Y-J, Ding F. Iterative solutions to matrix equations of the form AiXBi=Fi. Comput Math Appl. 2010;59:3500–3507. doi: 10.1016/j.camwa.2010.03.041
  • Ding F, Ding J. Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Appl Math Comput. 2008;197:41–50.
  • Ding F, Chen T-W. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans Automat Contr. 2005;50:1216–1221. doi: 10.1109/TAC.2005.852558
  • Ding F, Chen T-W. On iterative solutions of general coupled matrix equations. SIAM J Control Optim. 2006;44:2269–2284. doi: 10.1137/S0363012904441350
  • Ding F, Chen T-W. Iterative least-squares solutions of coupled Sylvester matrix equations. Syst Control Lett. 2005;54:95–107. doi: 10.1016/j.sysconle.2004.06.008
  • Wu A-G, Zeng X-L, Duan G-R, et al. Iterative solutions to the extended Sylvester-conjugate matrix equations. Appl Math Comput. 2010;217:130–142.
  • Wu A-G, Feng G, Duan G-R, et al. Iterative solutions to coupled Sylvester-conjugate matrix equations. Comput Math Appl. 2010;60:54–66. doi: 10.1016/j.camwa.2010.04.029
  • Song C-Q, Chen G-L, Zhao L-L. Iterative solutions to coupled Sylvester-transpose matrix equations. Appl Math Model. 2011;35:4675–4683. doi: 10.1016/j.apm.2011.03.038
  • Beik FPA, Mahmoud MM. Gradient-based iterative algorithm for solving the generalized coupled Sylvester-transpose and conjugate matrix equations over reflexive (anti-reflexive) matrices. Trans Inst Meas Control. 2014;36:99–110. doi: 10.1177/0142331213482485
  • Lv L-L, Chen J-B, Zhang L, et al. Gradient-based neural networks for solving periodic Sylvester matrix equations. J Franklin Inst. 2022;359:10849–10866. doi: 10.1016/j.jfranklin.2022.05.023
  • Li S-H, Ma C-F. Factor gradient iterative algorithm for solving a class of discrete periodic Sylvester matrix equations. J Franklin Inst. 2022;359:9952–9970. doi: 10.1016/j.jfranklin.2022.09.041
  • Fan W, Gu C-Q, Tian Z-L. Jacobi-gradient iterative algorithms for Sylvester matrix equations. In: Linear algebra society topics. Shanghai, China: Shanghai University; 2007. p. 16–20.
  • Niu Q, Wang X, Lu L-Z. A relaxed gradient based algorithm for solving Sylvester equations. Asian J Control. 2011;13:461–464. doi: 10.1002/asjc.v13.3
  • Huang B-H, Ma C-F. The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations. J Franklin Inst. 2018;355:3168–3195. doi: 10.1016/j.jfranklin.2018.02.014
  • Huang B-H, Ma C-F. On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations. J Franklin Inst. 2022;359:10688–10725. doi: 10.1016/j.jfranklin.2022.07.051
  • Wang W-L, Song C-Q, Ji S-P. Iterative solution to a class of complex matrix equations and its application in time-varying linear system. J Appl Math Comput. 2021;67:317–341. doi: 10.1007/s12190-020-01486-6
  • Ding F. Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl Math Model. 2013;37:1694–1704. doi: 10.1016/j.apm.2012.04.039
  • Wu A-G, Zhang Y, Qian Y-Y. Complex conjugate matrix equations. Beijing: Science Press; 2017.
  • Ding F, Chen T-W. Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica. 2005;41:315–325. doi: 10.1016/j.automatica.2004.10.010
  • Zhang H-M. A finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations by using the linear operators. J Franklin Inst. 2017;354:1856–1874. doi: 10.1016/j.jfranklin.2016.12.011