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Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System

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Abstract

This paper establishes some perturbation analysis for the tensor inverse, the tensor Moore-Penrose inverse, and the tensor system based on the t-product. In the settings of structured perturbations, we generalize the Sherman-Morrison-Woodbury (SMW) formula to the t-product tensor scenarios. The SMW formula can be used to perform the sensitivity analysis for a multilinear system of equations.

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Acknowledgements

The authors would like to thank two anonymous referees for their useful comments which led to significant improvements. We also deeply appreciate feedback on an earlier version of this manuscript from Professor Eric King-Wah Chu. This work is supported by the National Natural Science Foundation of China under grant number 11801534.

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China

    Zhengbang Cao & Pengpeng Xie

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  1. Zhengbang Cao
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  2. Pengpeng Xie
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Correspondence to Pengpeng Xie.

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Cao, Z., Xie, P. Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System. Commun. Appl. Math. Comput. 4, 1441–1456 (2022). https://doi.org/10.1007/s42967-022-00186-1

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  • DOI: https://doi.org/10.1007/s42967-022-00186-1

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