Computation of tensors generalized inverses under M-pro duct and applications

This paper introduces notions of the Drazin and core-EP inverses on tensors via Mpro duct. We propose a few properties of the Drazin and core-EP inverses of tensors, as well as effective tensor-based algorithms for calculating these inverses. In addition, definitions of composite generalized inverses are presented in the framework of the M-pro duct, including CMP, DMP, and MPD inverses of tensors. Tensorbased higher-order Gauss-Seidel and Gauss-Jacobi iterative methods are designed. Algorithms for these two iterative methods for solving multilinear equations have been developed. Certain multilinear systems are solved using the Drazin inverse, core-EP inverse, and composite generalized inverses, such as CMP, DMP, and MPD inverse. A tensor M-pro duct-based regularization technique is applied to solve the color image deblurring. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data