Perturbation analysis for t-product based tensor inverse, Moore-Penrose inverse and tensor system
Numerical Analysis
2021-08-17 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2107.09544,
title = {Perturbation analysis for t-product based tensor inverse, Moore-Penrose inverse and tensor system},
author = {Zhengbang Cao and Pengpeng Xie},
journal= {arXiv preprint arXiv:2107.09544},
year = {2021}
}