A Recommender Algorithm: Gradient Recurrent Neural Network Applied to Yang-Baxter-Like Equation

In this article, a traditional recommender algorithm termed gradient recurrent neural network (GRNN) model is introduced. Allowing for numerous practical problems such as the problems related to recommender systems or multi-agent systems that can be turned into matrix equation problems to resolve, the GRNN model becomes a more critical and promising role. The GRNN model, designed with the assistance of a square-norm-based energy function, is quite applicable to a recommender system and substantiated to be high-efficient in solving convex optimization linear or nonlinear problems. Simultaneously, implementing elaborately a theoretical analysis and numerical experiment computational simulation, the inherent exponential and stable convergence of the GRNN model is validated. With the aid of it, a theoretical nontrivial solution of the Yang-Baxter-like matrix equation $XAX=AXA$ can be obtained successfully.