Computation of tensors generalized inverses under $M$-product and applications
<|reference_start|>Computation of tensors generalized inverses under $M$-product and applications: This paper introduces notions of the Drazin and the core-EP inverses on tensors via M-product. 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-product, including CMP, DMP, and MPD inverse of tensors. Tensor-based higher-order Gauss-Seidel and Gauss-Jacobi iterative methods are designed. Algorithms for these two iterative methods to solve multilinear equations are developed. Certain multilinear systems are solved using the Drazin inverse, core-EP inverses, and composite generalized inverses such as CMP, DMP, and MPD inverse. A tensor M-product-based regularization technique is applied to solve the color image deblurring.<|reference_end|>
@article{sahoo2024computation,
    title={Computation of tensors generalized inverses under $M$-product and
  applications},
    author={Jajati Keshari Sahoo, Saroja Kumar Panda, Ratikanta Behera, Predrag S.
  Stanimirovi'c},
    journal={arXiv preprint arXiv:2405.16111},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.16111},
    primaryClass={math.NA cs.NA}
}