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arXiv · 2107.09544

Perturbation analysis for t-product based tensor inverse, Moore-Penrose inverse and tensor system

Zhengbang Cao·Pengpeng Xie
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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 sensitivity analysis for a multilinear system of equations.

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Zhengbang Cao, Pengpeng Xie. 2021-08-16. Perturbation analysis for t-product based tensor inverse, Moore-Penrose inverse and tensor system. https://arxiv.org/abs/2107.09544

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