arXiv subjects

Debasisha Mishra

Publications and source records attributed to Debasisha Mishra.

20 records · Page 2Linked to original sources

arXiv2016

Further results on generalized inverses of tensors via the Einstein product

The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A new method to compute the Moore-Penrose inverse of tensors is proposed. Reverse order laws for several generalized inverses of tensors are also presented. In addition to these, we discuss general solutions of multilinear systems of tensors using such theory.

math.RA↗

arXiv2016

Proper Weak Regular Splitting and its Application to Convergence of Alternating Iterations

The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular matrices. Secondly, we propose an alternating iterative method for solving rectangular linear systems by using the Moore-Penrose inverse and discuss its convergence theory, by extending the work of Benzi and Szyld Numererische Mathematik 76 (1997) 309-321; MR1452511]. Furthermore, a comparison result is obtained which insures faster convergence rate of the proposed alternating iterative scheme.

math.NA↗