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

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Hassan Bozorgmanesh, Masoud Hajarian

Published: 2022, Last Modified: 15 Aug 2025J. Sci. Comput. 2022EveryoneRevisionsBibTeXCC BY-SA 4.0
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.