Computing Tensor Generalized bilateral inverses
Numerical Analysis
2023-11-30 v1 Numerical Analysis
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 TGBI were studied and verified using a specific algebraic approach. Further, a few characterizations of known CGIs (such as CMP, DMP, MPD, MPCEP, and CEPMP) are derived. The main properties of the TGBIs ware exploited and verified through numerical examples.
Keywords
Cite
@article{arxiv.2311.17556,
title = {Computing Tensor Generalized bilateral inverses},
author = {Ratikanta Behera and Jajati Keshari Sahoo and Predrag S. Stanimirovic and Alena Stupina and Artem Stupin},
journal= {arXiv preprint arXiv:2311.17556},
year = {2023}
}
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18 pages