@article {20108,
	title = {One-sided weighted outer inverses of tensors},
	journal = {Journal of Computational and Applied Mathematics},
	year = {2020},
	month = {2020},
	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.},
	keywords = {Einstein product, Multidimensional array, Outer inverse, Tensor equation, Tensor rank},
	isbn = {0377-0427},
	url = {http://www.sciencedirect.com/science/article/pii/S0377042720305847},
	author = {Mosi{\'c}, Dijana and Predrag S. Stanimirovi{\'c} and Jajati Keshari Sahoo and Ratikanta Behera and Vasilios N. Katsikis}
}
