One-sided weighted outer inverses of tensors

Mosić, Dijana; Predrag S. Stanimirović; Jajati Keshari Sahoo; Ratikanta Behera; Vasilios N. Katsikis

One-sided weighted outer inverses of tensors

Citation:

Mosić, D., Stanimirović, P. S., Sahoo, J. K., Behera, R., & Katsikis, V. N. (2020). One-sided weighted outer inverses of tensors. Journal of Computational and Applied Mathematics. presented at the 2020. Copy at http://www.tinyurl.com/yycyqnfa

Abstract:

In this paper, for the first time in literature, we introduce one-sided weighted inverses and extend the notions of one-sided inverses, outer inverses and inverses along given elements. Although our results are new and in the matrix case, we decided to present them in tensor space with reshape operator. For this purpose, a left and right (M,N)-weighted (B,C)-inverse and the (M,N)-weighted (B,C)-inverse of a tensor are defined. Additionally, necessary and sufficient conditions for the existence of these new inverses are presented. We describe the sets of all left (or right) (M,N)-weighted (B,C)-inverses of a given tensor. As consequences of these results, we consider the one-sided (B,C)-inverse, (B,C)-inverse, one-sided inverse along a tensor and inverse along a tensor. Further, we introduce a (M,N)-weighted (B,C)-outer inverse and a W-weighted (B,C)-outer inverse of tensors with a few characterizations. Then, corresponding algorithms for computing various types of outer inverses of tensors are proposed, implemented and tested. The prowess of the proposed inverses are demonstrated for finding the solution of Poisson problem and the restoration of 3D color images.

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National and Kapodistrian University of Athens
Office: 601 (Floor 6)
Phone number: (+30) 210-3689489
Address: Sofokleous 1, 10559, Athens, Greece
Email: vaskatsikis@econ.uoa.gr
URL: http://scholar.uoa.gr/vaskatsikis
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Vasilios Katsikis

Professor, Economics

One-sided weighted outer inverses of tensors

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