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

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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.

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Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their valuable comments that improved the quality of the paper.

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  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    Hassan Bozorgmanesh & Masoud Hajarian

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  1. Hassan Bozorgmanesh
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  2. Masoud Hajarian
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Correspondence to Masoud Hajarian.

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Bozorgmanesh, H., Hajarian, M. Triangular Decomposition of CP Factors of a Third-Order Tensor with Application to Solving Nonlinear Systems of Equations. J Sci Comput 90, 74 (2022). https://doi.org/10.1007/s10915-021-01758-8

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