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Numerical study on Moore-Penrose inverse of tensors via Einstein product

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Abstract

The notation of Moore-Penrose inverse of matrices has been extended from matrix space to even-order tensor space with Einstein product. In this paper, we give the numerical study on the Moore-Penrose inverse of tensors via the Einstein product. More precisely, we transform the calculation of Moore-Penrose inverse of tensors via the Einstein product into solving a class of tensor equations via the Einstein product. Then, by means of the conjugate gradient method, we obtain the approximate Moore-Penrose inverse of tensors via the Einstein product. Finally, we report some numerical examples to show the efficiency of the proposed methods and testify the conclusion suggested in this paper.

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Funding

This research is supported by China Postdoctoral Science Foundation (Grant No. 2019M660203) and National Natural Science Foundation of China (Grant Nos. 12001211, 12071159, 61976053)

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Baohua Huang

  2. College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Baohua Huang

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  1. Baohua Huang
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Correspondence to Baohua Huang.

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Huang, B. Numerical study on Moore-Penrose inverse of tensors via Einstein product. Numer Algor 87, 1767–1797 (2021). https://doi.org/10.1007/s11075-021-01074-0

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  • DOI: https://doi.org/10.1007/s11075-021-01074-0

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