Triangular Decomposition of CP Factors of a Third-Order Tensor with Application to Solving Nonlinear Systems of Equations

摘要

Abstract In this paper, we focus on multi-linear systems of equations with a third-order CP-decomposed coefficient tensor, applying the LU decomposition on its factor matrices, a more easily solvable system is obtained. Also, a result on the number of solutions for a multi-linear system with a CP-decomposed tensor is given for different ranks of tensors and an application of the proposed algorithm for solving nonlinear systems is presented. In the end, numerical results are provided.