arXiv subjects

Ashish Kumar Nandi

Publications and source records attributed to Ashish Kumar Nandi.

6 recordsLinked to original sources

arXiv2026

Direct Methods for Singular Fuzzy Linear Systems Using Generalized Inverses and Its Applications

Fuzzy matrices provide an effective framework for modeling uncertainty in scientific and engineering problems, particularly fuzzy linear systems. This work transforms a general FLS into a crisp linear system using an embedding approach and reduces it to a standard block structured form via column operations. A direct LU decomposition is developed under suitable range conditions, enabling the computation of minimum norm solutions of rectangular FLS using the generalized inverses. A full rank decomposition is further proposed to compute the Moore Penrose inverse for arbitrary rectangular matrices, and consistency conditions for these inverses are established. A unified framework for obtaining strong fuzzy solutions based on monotonicity and non-negativity constraints are presented. Efficient algorithms based on LU, QR, and SVD decompositions are developed for the block structured matrix. The applicability and computational efficiency of the proposed methods are demonstrated through fuzzy circuit equations and Markov chain processes.

math.GM↗

arXiv2025

On Characterizations of W-weighted DMP and MPD Inverses

Recently, the weak Drazin inverse and its characterization have been crucial studies for matrices of index k. In this article, we have revisited W-weighted DMP and MPD inverses and constructed a general class of unique solutions to certain matrix equations. Moreover, we have generalized the W-weighted Drazin inverse of Meng, 2017 using the minimal rank Wweighted weak Drazin inverse. In addition to that, we have derived several equivalent properties of W-weighted DMP and MPD inverses for minimal rank W-weighted weak Drazin inverse of rectangular matrices. Furthermore, some projection-based results are discussed for the characterization of minimal rank W-weighted Drazin inverse, along with some new expressions that are derived for MPD and DMP inverses. Thereby, we have elaborated certain expressions of the perturbation formula for W-weighted weak MPD and DMP inverses. As an application, we establish the reverse and forward order laws using the W-weighted weak Drazin inverse and the minimal rank W-weighted weak Drazin inverse, and apply these results to solve certain matrix equation.

math.RA↗

arXiv2020

Alternating Stationary Iterative Methods Based on Double Splittings

Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Splitting (ADS) schemes formulated by two double splittings and then alternating the respective iterations. The convergence conditions are then discussed along with comparative analysis. The set of double splittings used in each ADS schemes induce a preconditioned system which helps in showing the convergence of the ADS schemes. We also show that the classes of matrices for which one ADS scheme is better than the other are mutually exclusive. Numerical experiments confirm the proposed ADS schemes are superior to the existing methods in actual implementation. Though the problems are considered in the rectangular matrix settings, the same problems are even new in non-singular matrix settings.

math.NA↗

arXiv2020

Regularized Iterative Method for Ill-posed Linear Systems Based on Matrix Splitting

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The convergence of such a well-posed system is discussed by using different types of matrix splittings. Comparison analysis of both systems are studied by operating certain types of weak splittings. Further, we have extended the double splitting of [Song J and Song Y, Calcolo 48(3), 245-260, 2011] to double weak splitting of type II for nonsingular symmetric matrices. In addition to that, some more comparison results are presented with the help of such weak double splittings of type I and type II.

math.NA↗

arXiv2019

Further results on the Drazin inverse of even-order tensors

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.

math.NA↗

arXiv2018

Three-step alternating iterations for index one matrices

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 with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step alternating iterations using proper splittings and group inverses to find an approximate solution of singular linear systems, iteratively. A preconditioned alternating iterative scheme is also proposed to relax some sufficient conditions and to obtain faster convergence as well. We then show that our scheme converges faster than the existing one. The theoretical findings are then validated numerically.

math.NA↗