Two Modified Newton-Raphson Iteration Algorithms for Yang-Baxter-like Matrix Equation with Step-Size Analyses

This paper mainly proposes two Modified Newton-Raphson iterated (MNRI) algorithms to solve the Yang-Baxter-like equation indirectly and directly, respectively. Deriving from the zero finding conception, the MNRI algorithm shares similar formulation of the Newton-Raphson iterated algorithm with various step-sizes which determine the convergence property. Moreover, the system model is also presented in this paper, which demonstrates the principle of the MNRI algorithm to update the computed solution. Lastly, The theoretical analyses and the simulation verifications of the MNRI algorithms are provided to demonstrate its superiority and efficiency.