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

Zhengbang Cao; Pengpeng Xie

doi:10.1007/s42967-022-00186-1

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4) : 1441 -1456. DOI: 10.1007/s42967-022-00186-1

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

Zhengbang Cao ¹
, Pengpeng Xie ¹^,b

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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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Zhengbang Cao, Pengpeng Xie. Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System. Communications on Applied Mathematics and Computation, 2022, 4(4): 1441-1456 DOI:10.1007/s42967-022-00186-1