Computing Tensor Generalized Bilateral Inverses

doi:10.1007/s42967-024-00373-2

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (6): 2269-2288.doi: 10.1007/s42967-024-00373-2

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Computing Tensor Generalized Bilateral Inverses

Ratikanta Behera¹, Jajati Keshari Sahoo², Predrag S. Stanimirović^3,4, Alena Stupina⁴, Artem Stupin⁴

1. Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India;
2. Department of Mathematics, Birla Institute of Technology and Science Pilani, K. K. Birla Goa Campus, Goa, India;
3. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia;
4. Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041, Krasnoyarsk, Russian Federation

收稿日期:2023-08-31 修回日期:2024-01-14 发布日期:2025-12-24
通讯作者: Predrag S. Stanimirović, E-mail:pecko@pmf.ni.ac.rs E-mail:pecko@pmf.ni.ac.rs
基金资助:
This research is supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2022-1121).

Computing Tensor Generalized Bilateral Inverses

Ratikanta Behera¹, Jajati Keshari Sahoo², Predrag S. Stanimirović^3,4, Alena Stupina⁴, Artem Stupin⁴

1. Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India;
2. Department of Mathematics, Birla Institute of Technology and Science Pilani, K. K. Birla Goa Campus, Goa, India;
3. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia;
4. Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041, Krasnoyarsk, Russian Federation

Received:2023-08-31 Revised:2024-01-14 Published:2025-12-24
Contact: Predrag S. Stanimirović, E-mail:pecko@pmf.ni.ac.rs E-mail:pecko@pmf.ni.ac.rs
Supported by:
This research is supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2022-1121).

摘要/Abstract

摘要： 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.

关键词: Generalized bilateral inverses (GBIs), Einstein product, Outer inverse, Poisson equations

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.

Key words: Generalized bilateral inverses (GBIs), Einstein product, Outer inverse, Poisson equations

中图分类号:

Ratikanta Behera, Jajati Keshari Sahoo, Predrag S. Stanimirović, Alena Stupina, Artem Stupin. Computing Tensor Generalized Bilateral Inverses[J]. Communications on Applied Mathematics and Computation, 2025, 7(6): 2269-2288.

参考文献

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Computing Tensor Generalized Bilateral Inverses

Computing Tensor Generalized Bilateral Inverses

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