On sign function of tensors with Einstein product and its application in solving Yang-Baxter tensor equation

In recent years, tensor problems have been studied in multiple fields of science and engineering including applied mathematics, the theory of completely integrable quantum, data mining, statistics, physics, chemistry, machine learning, medical engineering, and others. In machine learning, the word tensor informally refers to two different concepts that organize and represent data. In this work, at first, the concept of the sign function of a tensor is developed using the sign function of a matrix. Then, we propose an iterative method to find the sign function of a tensor. We prove that the order of convergence of the proposed method is three. Finally, we extend the iterative method for solving the Young-Baxter equation, which has many applications in fully integrable quantum theory, classical systems, and exactly solvable models of statistical physics. The accuracy and effectiveness of the proposed method in comparison to well-known methods are demonstrated by various numerical examples.