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Computing Tensor Generalized Bilateral Inverses

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Abstract

We introduce tensor generalized bilateral inverses (TGBIs) under the Einstein tensor product as an extension of generalized bilateral inverses (GBIs) in the matrix environment. Moreover, the TBGI class includes so far considered composite generalized inverses (CGIs) for matrices and tensors. Applications of TBGIs for solving multilinear systems are presented. The characterizations and representations of the TGBI were studied and verified using a specific algebraic approach. Further, a few characterizations of known CGIs (such as the CMP, DMP, MPD, MPCEP, and CEPMP) are derived. The main properties of the TGBIs were exploited and verified through numerical examples.

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Acknowledgements

The authors are grateful to referees for the useful comments which improved the paper and for understanding during the revision.

Funding

Ratikanta Behera is supported by the Science and Engineering Research Board (SERB), Department of Science and Technology, India (Grant No. EEQ/2022/001065). Jajati Keshari Sahoo is supported by the Science and Engineering Research Board (SERB), Department of Science and Technology, India (Grant No. SUR/2022/004357). Predrag Stanimirović is supported by the Science Fund of the Republic of Serbia (Grant No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications-QUAM). This research is supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2022-1121).

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Authors and Affiliations

  1. Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India

    Ratikanta Behera

  2. Department of Mathematics, Birla Institute of Technology and Science Pilani, K. K. Birla Goa Campus, Goa, India

    Jajati Keshari Sahoo

  3. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

    Predrag S. Stanimirović

  4. Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041, Krasnoyarsk, Russian Federation

    Predrag S. Stanimirović, Alena Stupina & Artem Stupin

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  1. Ratikanta Behera
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  2. Jajati Keshari Sahoo
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  3. Predrag S. Stanimirović
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Correspondence to Predrag S. Stanimirović.

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Behera, R., Sahoo, J.K., Stanimirović, P.S. et al. Computing Tensor Generalized Bilateral Inverses. Commun. Appl. Math. Comput. (2024). https://doi.org/10.1007/s42967-024-00373-2

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  • DOI: https://doi.org/10.1007/s42967-024-00373-2

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