In this paper, a conjugate gradient iterative method based on tensor calculation is proposed for obtaining the symmetric solutions of a special Sylvester tensor equation  Without rounding errors, for any given initial symmetric tensor, the sequence of tensors obtained by the proposed algorithm converges to a symmetric solution (the least-squares symmetric solution). Finally, numerical examples are provided to illustrate the validity and feasibility of the algorithm.

Sylvester tensor equation, iterative algorithm, symmetric solution, least-squares symmetric solution, Einstein product.

Received: March 1, 2021; Accepted: April 1, 2021; Published: April 28, 2021

How to cite this article: Qun Meng and Yu-Zhu Xie, Iterative algorithms for the symmetric and least-squares symmetric solutions of a tensor equation, JP Journal of Algebra, Number Theory and Applications 50(2) (2021), 179-212. DOI: 10.17654/NT050010179

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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