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Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of tensors over a commutative ring and a noncommutative ring. Several numerical examples are provided in support of the theoretical results. We also propose algorithms for computing the inner inverses, the Moore–Penrose inverse, and weighted Moore–Penrose inverse of tensors over a noncommutative ring. The prowess of some of the results is demonstrated by applying these ideas to solve an image deblurring problem. [ABSTRACT FROM AUTHOR]

A novel complex varying‐parameter finite‐time zeroing neural network (VPFTZNN) for finding a solution to the time‐dependent division problem is introduced. A comparative study in relation to the zeroing neural network (ZNN) and finite‐time zeroing neural network (FTZNN) is established in terms of the error function and the convergence speed. The error graphs of the VPFTZNN design show promising results and perform better than corresponding ZNN and FTZNN graphs. The proposed dynamical systems are suitable tools for overcoming the division by zero difficulty, which appears in the time‐varying division. An application of the introduced VPFTZNN model in an output tracking control time‐varying linear system is demonstrated. [ABSTRACT FROM AUTHOR]

Summary: The notion of the Drazin inverse of an even‐order tensors 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 establishing a few characterizations of the Drazin inverse and 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 of multilinear systems by using the Drazin inverse and iterative (higher order Gauss‐Seidel) method of tensors. Besides these, the convergence analysis of the iterative technique is also investigated within the framework of the Einstein product. [ABSTRACT FROM AUTHOR]