Further results on the Drazin inverse of even-order tensors
For researchers in tensor algebra and multilinear systems, this work incrementally advances the theoretical and computational understanding of Drazin inverses for tensors.
This paper extends the theory of Drazin inverses for even-order tensors under the Einstein product, providing new characterizations, computation methods via generalized inverses and full rank decomposition, and applying the Drazin inverse to solve multilinear systems with an iterative Gauss-Seidel method, including convergence analysis.
The notion of the Drazin inverse of an even-order tensor with the Einstein product was introduced, very recently [J. Ji and Y. Wei. Comput. Math. Appl., 75(9), (2018), pp. 3402-3413]. In this article, we further elaborate this theory by producing a few characterizations of the Drazin inverse and the W-weighted Drazin inverse of tensors. In addition to these, we compute the Drazin inverse of tensors using different types of generalized inverses and full rank decomposition of tensors. We also address the solution to the multilinear systems using the Drazin inverse and iterative (higher order Gauss-Seidel) method of tensors. Besides this, the convergence analysis of the iterative technique is also investigated within the framework of the Einstein product.