%0 Journal Article %T An efficient iterative algorithm for finding a nontrivial symmetric solution of the Yang-Baxter-like matrix equation %A Chacha, Chacha Stephen %A Kim, Hyun-Min %J Journal of Nonlinear Sciences and Applications %D 2019 %V 12 %N 1 %@ ISSN 2008-1901 %F Chacha2019 %X This paper presents an efficient iterative method to obtain a nontrivial symmetric solution of the Yang-Baxter-like matrix equation \(AXA=XAX \). Necessary conditions for the convergence of the propounded iterative method are derived. Finally, three numerical examples to illustrate the efficiency of the proposed method and the preciseness of our theoretical results are provided. %9 journal article %R 10.22436/jnsa.012.01.02 %U http://dx.doi.org/10.22436/jnsa.012.01.02 %P 21--29 %0 Journal Article %T A family of solutions of the Yang-Baxter equation %A D. Bachiller %A F. Cedó %J J. Algebra %D 2014 %V 412 %F Bachiller2014 %0 Journal Article %T Partition function of the eight–vertex lattice model %A R. J. Baxter %J Ann. Physics %D 1972 %V 70 %F Baxter1972 %0 Journal Article %T Retractability of set theoretic solutions of the Yang-Baxter equation %A F. Cedó %A E. Jespers %A J. Okniski %J Adv. Math. %D 2010 %V 224 %F Cedó2010 %0 Journal Article %T A nontrivial solution to a stochastic matrix equation %A J. Ding %A N. H. Rhee %J East Asian J. Appl. Math. %D 2012 %V 2 %F Ding2012 %0 Journal Article %T Computing solutions of the Yang-Baxter-like matrix equation for diagonalisable matrices %A J. Ding %A N. H. Rhee %J East Asian J. Appl. Math. %D 2015 %V 5 %F Ding2015 %0 Journal Article %T Spectral solutions of the Yang–Baxter matrix equation %A J. Ding %A N. H. Rhee %J J. Math. Anal. Appl. %D 2013 %V 402 %F Ding2013 %0 Journal Article %T Solving the YangBaxter–like matrix equation for a class of elementary matrices %A J. Ding %A H. Tian %J Comput. Math. Appl. %D 2016 %V 72 %F Ding2016 %0 Journal Article %T On the structure of the spectral solutions of the Yang–Baxter matrix equation %A J. Ding %A C. Zhang %J Appl. Math. Lett. %D 2014 %V 35 %F Ding2014 %0 Journal Article %T Further solutions of a Yang-Baxter–like matrix equation %A J. Ding %A C. Zhang %A N. H. Rhee %J East Asian J. Appl. Math. %D 2013 %V 2 %F Ding2013 %0 Journal Article %T Commuting solutions of the Yang-Baxter matrix equation %A J. Ding %A C. Zhang %A N. H. Rhee %J Appl. Math. Lett. %D 2015 %V 44 %F Ding2015 %0 Journal Article %T Eigenvalues of rank-one updated matrices with some applications %A J. Ding %A A. Zhou %J Appl. Math. Lett. %D 2007 %V 20 %F Ding2007 %0 Journal Article %T Complete commuting solutions of the Yang-Baxter-like matrix equation for diagonalizable matrices %A Q. Dong %A J. Ding %J Comput. Math. Appl. %D 2016 %V 72 %F Dong2016 %0 Book %T Nonlinear Equations, Quantum Groups and Duality Theorems: A Primer on the Yang-Baxter Equation %A F. Felix %D 2009 %I VDM Verlag %C Germany %F Felix 2009 %0 Journal Article %T Quadratic algebras, Yang-Baxter equation, and Artin–Schelter regularity %A T. Gateva–Ivanova %J Adv. Math. %D 2012 %V 230 %F Gateva–Ivanova2012 %0 Journal Article %T All solutions to the constant quantum Yang-Baxter equation in two dimensions %A J. Hietarinta %J Phys. Lett. A %D 1992 %V 165 %F Hietarinta 1992 %0 Book %T Yang-Baxter Equation in Integrable Systems %A M. Jimbo %D 1989 %I World Scientific Publishing Co. %C Teaneck %F Jimbo1989 %0 Journal Article %T Solutions of the Yang-Baxter equation, in: Yang-Baxter Equation in Integrable Systems %A P. P. Kulish %A E. K. Sklyanin %J Adv. Series in Math. Phys. %D 1990 %V 10 %F Kulish1990 %0 Journal Article %T Explicit solutions of the Yang–Baxter–like matrix equation for an idempotent matrix %A S. I. A. Mansour %A J. Ding %A Q. L. Huang %J Appl. Math. Lett. %D 2017 %V 63 %F Mansour2017 %0 Journal Article %T All solutions of the Yang–Baxter–like matrix equation for rank-one matrices %A H. Tian %J Appl. Math. Lett. %D 2016 %V 51 %F Tian2016 %0 Journal Article %T Some exact results for the many–body problem in one dimension with repulsive delta–function interaction %A C. N. Yang %J Phys. Rev. Lett. %D 1967 %V 19 %F Yang1967 %0 Book %T Braid Group, Knot Theory, and Statistical Mechanics %A C. Yang %A M. Ge %D 1989 %I World Scientific Publishing Co. %C Teaneck %F Yang1989