60 citations · 155 across the 16 of their papers we have counts for
17 papers
On WD and WDMP generalized inverses in rings
Amit Kumar, Debasisha Mishra
Motivated by the very recent work of Gao, Y., Chen, J., Wang, J., Zou, H. [Comm. Algebra, 49(8) (2021) 3241-3254; MR4283143], we introduce two new generalized inverses named weak D…
On generalized-Drazin inverses and GD-star matrices
Amit Kumar, Vaibhav Shekhar, Debasisha Mishra
Motivated by the works of Wang and Liu [Linear Algebra Appl., 488 (2016) 235-248; MR3419784] and Mosic [Results Math., 75(2) (2020) 1-21; MR4079761], we provide further results on…
Numerical range for weighted Moore-Penrose inverse of tensor
Aaisha Be, Vaibhav Shekhar, Debasisha Mishra
This article first introduces the notion of weighted singular value decomposition (WSVD) of a tensor via the Einstein product. The WSVD is then used to compute the weighted Moore-P…
On forward-order law for core inverse in rings
Amit Kumar, Debasisha Mishra
If and are a pair of invertible elements, then is also invertible and the inverse of the product satisfying is known as the {\it forwar…
A note on numerical ranges of tensors
Nirmal Chandra Rout, Krushnachandra Panigrahy, Debasisha Mishra
Theory of numerical range and numerical radius for tensors is not studied much in the literature. In 2016, Ke {\it et al.} [Linear Algebra Appl., 508 (2016) 100-132] introduced fir…
Further results on -numerical radius inequalities
Nirmal Chandra Rout, Debasisha Mishra
Let be a bounded linear positive operator on a complex Hilbert space Further, let denote the set of all bounded linear operators on…
Convergence of two-stage iterative scheme for -weak regular splittings of type II with application to Covid-19 pandemic model
Vaibhav Shekhar, Nachiketa Mishra, Debasisha Mishra
Monotone matrices play a key role in the convergence theory of regular splittings and different types of weak regular splittings. If monotonicity fails, then it is difficult to gua…
Alternating Stationary Iterative Methods Based on Double Splittings
Ashish Kumar Nandi, Nachiketa Mishra, Debasisha Mishra
Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Split…
On A-numerical radius inequalities for operator matrices
Nirmal Chandra Rout, Satyajit Sahoo, Debasisha Mishra
Let ( be a complex Hilbert space and be a positive bounded linear operator on it. Let be the -numerical radius and be…
Reverse-order law for weighted Moore--Penrose inverse of tensors
Krushnachandra Panigrahy, Debasisha Mishra
In this paper, we provide a few properties of the weighted Moore--Penrose inverse for an arbitrary order tensor via the Einstein product. We again obtain some new sufficient condit…
Three-step alternating iterations for index one matrices
Ashish Kumar Nandi, Jajati Keshari Sahoo, Debasisha Mishra
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal wit…
On reverse-order law of tensors and its application to additive results on Moore-Penrose inverse
Krushnachandra Panigrahy, Debasisha Mishra
The equality $(\mc{A}\n\mc{B})^\dagger = \mc{B}^\dagger \n \mc{A}^\dagger$ for any two complex tensors $\mc{A}$ and $\mc{B}$ of arbitrary order, is called as the {\it reverse-order…
An extension of the Moore-Penrose Inverse of a Tensor via the Einstein product
Krushnachandra Panigrahy, Debasisha Mishra
In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a te…
Reverse order law for the Moore-Penrose inverses of tensors
Krushnachandra Panigrahy, Ratikanta Behera, Debasisha Mishra
Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-P…
Comparison results for proper multisplittings of rectangular matrices
Chinmay Kumar Giri, Debasisha Mishra
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an i…
Further results on generalized inverses of tensors via the Einstein product
Ratikanta Behera, Debasisha Mishra
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 chara…
Proper Weak Regular Splitting and its Application to Convergence of Alternating Iterations
Debasisha Mishra
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 revi…