Ratikanta Behera

Ratikanta Behera
Indian Institute of Science | IISC · Division of Mathematical and Physical Sciences

PhD

About

41
Publications
4,735
Reads
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372
Citations
Citations since 2016
35 Research Items
365 Citations
2016201720182019202020212022020406080100
2016201720182019202020212022020406080100
2016201720182019202020212022020406080100
2016201720182019202020212022020406080100
Additional affiliations
December 2019 - May 2022
University of Central Florida
Position
  • PostDoc Position
July 2016 - December 2019
Indian Institute of Science Education and Research Kolkata
Position
  • Professor (Assistant)
January 2015 - July 2016
University Joseph Fourier - Grenoble 1
Position
  • PostDoc Position
Education
November 2006 - February 2008
Utkal University
Field of study
  • Mathematics
July 2004 - July 2006
Utkal University
Field of study
  • Mathematics

Publications

Publications (41)
Article
The notion of the weighted core inverse in a ring with involution was introduced recently [Mosić et al. Comm. Algebra, 2018; 46(6); 2332-2345]. In this paper, we explore new characterizations of the weighted core inverse of sum and the difference between two weighted core invertible elements in a ring with involution under different conditions. Fur...
Preprint
Mosic and Djordjevic introduced the notation of the gDMP inverse for Hilbert space operators in [J. Spectr. Theory, 8(2):555-573, 2018] by considering generalized Drazin inverse with the Moore-Penrose inverse. This paper introduces two new classes of inverses: GD1 (generalized Drazin and inner) inverse and 1GD (inner and generalized Drazin) inverse...
Article
A robust noise-tolerant zeroing neural network (ZNN) is introduced for solving time-varying linear matrix equations (TVLME). The convergence speed of designed neural dynamics is analyzed theoretically and compared with the convergence of neural networks which include traditional activation functions, such as the tunable activation function, versati...
Article
Following the popularity of the core-EP (c-EP) and weighted core-EP (w-c-EP) inverses, so called one-sided versions of the w-c-EP inverse are introduced recently in Behera et al. (Results Math 75:174 (2020). These extensions are termed as E-w-c-EP and F-w-d-c-EP g-inverses as well as the star E-w-c-EP and the F-w-d-c-EP star classes of g-inverses....
Article
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 rin...
Article
A family of varying-parameter finite-time zeroing neural networks (VPFTZNN) is introduced for solving the time-varying Sylvester equation (TVSE). The convergence speed of the proposed VPFTZNN family is analysed and compared with the traditional zeroing neural network (ZNN) and the finite-time zeroing neural network (FTZNN). The behaviour of the pro...
Article
In this paper, we introduce the notion of outer generalized inverses, with predefined range and null space, of tensors with rational function entries equipped with the Einstein product over an arbitrary field, of characteristic zero, with or without involution. We assume that the involved tensor entries are rational functions of unassigned variable...
Article
In this paper, for the first time in literature, we introduce one-sided weighted inverses and extend the notions of one-sided inverses, outer inverses and inverses along given elements. Although our results are new and in the matrix case, we decided to present them in tensor space with reshape operator. For this purpose, a left and right (M,N)-weig...
Article
A class of adaptive recurrent neural networks (RNN) for computing the inverse of a time-varying matrix with accelerated convergence time is defined and considered. The proposed neural dynamic model involves an exponential gain time-varying term in the nonlinear activation of the finite-time Zhang neural network (FTZNN) dynamical equation. Individua...
Article
Full-text available
In this paper, we introduce the notation of E-weighted core-EP and F-weighted dual core-EP inverse of matrices. We then obtain a few explicit expressions for the weighted core-EP inverse of matrices through other generalized inverses. Further, we discuss the existence of generalized weighted Moore-Penrose inverse and additive properties of the weig...
Article
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 er...
Preprint
The notion of weighted $(b,c)$-inverse of an element in rings were introduced, very recently [Comm. Algebra, 48 (4) (2020): 1423-1438]. In this paper, we further elaborate on this theory by establishing a few characterizations of this inverse and their relationships with other $(v, w)$-weighted $(b,c)$-inverses. We introduce some necessary and suff...
Article
To extend the notation of inner inverses, we define weighted inner inverses of a rectangular matrix. In particular, we introduce a W-weighted (B, C)-inner inverse of A, for given matrices A, W, B, C, and present some characterizations and conditions for its existence. Since this new inverse is not unique, we describe the set of all W-weighted (B, C...
Article
Full-text available
Within the field of multilinear algebra, inverses and generalized inverses of tensors based on the Einstein product have been investigated over the past few years. The notion of the weighted Moore–Penrose inverses of even-order tensors in the framework of the Einstein product was introduced recently (Ji and Wei in Front Math China 12(6):1319–1337,...
Article
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...
Article
In this paper, we introduce new representations and characterizations of the outer inverse of tensors through QR decomposition. Derived representations are usable in generating corresponding representations of main tensor generalized inverses. Some results on reshape operation of a tensor are added to the existing theory. An effective algorithm for...
Preprint
Full-text available
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 non-commutative ri...
Preprint
Full-text available
In this paper, we introduce the notion of weak core and central weak core inverse in a proper $*$-ring. We further elaborate on these two classes by producing a few representation and characterization of the weak core and central weak core invertible elements. We investigate additive properties and a few explicit expressions for these two classes o...
Preprint
Full-text available
In this paper, we introduce the notation of $E$-weighted core-EP and $F$-weighted dual core-EP inverse of matrices. We then obtain a few explicit expressions for the weighted core-EP inverse of matrices through other generalized inverses. Further, we discuss the existence of generalized weighted Moore-Penrose inverse and additive properties of the...
Preprint
Full-text available
The notion of the weighted core inverse in a ring with involution was introduced, recently [Mosic et al. Comm. Algebra, 2018; 46(6); 2332-2345]. In this paper, we explore new representation and characterization of the weighted core inverse of sum and difference of two weighted core invertible elements in an unital ring with involution under differe...
Article
The notion of the core inverse of tensors with the Einstein product was introduced, very recently (Sahoo et al. Comp Appl Math 39:9, 2020). In this paper we establish a few sufficient and necessary conditions for reverse-order law of this inverse. Further, we discuss mixed-type reverse-order law for core inverse. In addition to these, we discuss co...
Article
Applications of the theory and computations of Boolean matrices are of fundamental importance to study a variety of discrete structural models. But the increasing ability of data collection systems to store huge volumes of multidimensional data, the Boolean matrix representation of data analysis is not enough to represent all the information conten...
Article
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific algebraic approach, based on proposed definitions and previously verified properties. The approach used here is new...
Preprint
Full-text available
In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Then, we study some properties of the one-sided core and dual-core inverse of matrices along with group inverse and weighted Moore-Penrose inverse. Further, by applying the new representation and properties of the weighted core inverse of t...
Preprint
Full-text available
The notion of the core inverse of tensors with the Einstein product was introduced, very recently. This paper we establish some sufficient and necessary conditions for reverse-order law of this inverse. Further, we present new results related to the mixed-type reverse-order law for core inverse. In addition to these, we discuss core inverse solutio...
Preprint
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific algebraic approach, based on proposed definitions and previously verified properties. The approach used here is new...
Preprint
Full-text available
The notion of the Drazin inverse of an even-order tensor with the Einstein product was introduced, very recently. In this article, we further elaborate this theory by producing 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...
Preprint
Applications of the theory and computations of boolean matrices are of fundamental importance to study a variety of discrete structural models. But the increasing ability of data collection systems to store huge volumes of multidimensional data, the boolean matrix representation of data analysis is not enough to represent all the information conten...
Preprint
Full-text available
We explore the singular value decomposition and full rank decomposition of arbitrary-order tensors using reshape operation. Here the treatment of arbitrary-order is a straightforward task due to the nature of the isomorphism between arbitrary-order tensor spaces and matrix spaces. Within the framework, the Moore-Penrose and weighted Moore-Penrose i...
Article
In this paper, we present a numerical simulation of a convection-dominated problem using adaptive wavelet collocation method. This is based on second-generation spherical wavelets on a recursively refined spherical geodesic grid. The power lies in the fact that they only require small number of coefficients to represent this problem more accurately...
Article
We put forth a dynamic computing framework for scale-selective adaptation of weighted essential non-oscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet based multiresolution (MR) procedure, embedded in a conservative finite volume formulation, is used for a two-fold p...
Article
Full-text available
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-Penrose inverse of tensors. We then obtain a few necessary and sufficient conditions for the reverse order law for the Moore-Penrose inverse of tensors via the Einstein pr...
Article
Full-text available
The notion of the Moore–Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate on 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 gen...
Article
Full-text available
In this work, a new adaptive multi-level approximation of surface divergence and scalar-valued surface curl operator on a recursively refined spherical geodesic grid is presented. A hierarchical finite volume scheme based on the wavelet multi-level decomposition is used to approximate the surface divergence and scalar-valued surface curl operator....
Article
In this paper, we present a theoretical analysis of the synchrosqueezing transform adapted to multicomponent signals made of strongly frequency modulated modes, which was recently proposed in the short time Fourier transform framework [13]. Before dealing in detail with the theoretical aspect, we explain throughout numerical simulations why the hyp...
Article
Full-text available
This work presents a new adaptive multilevel approximation of the gradient operator on a recursively refined spherical geodesic grid. The multilevel structure provides a simple way to adapt the computation to the local structure of the gradient operator so that high resolution computations are performed only in regions where singularities or sharp...
Article
Full-text available
In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based...
Article
Full-text available
In this paper, we apply wavelet optimized finite difference method to solve modified Camassa–Holm and modified Degasperis–Procesi equations. The method is based on Daubechies wavelet with finite difference method on an arbitrary grid. The wavelet is used at regular intervals to adaptively select the grid points according to the local behaviour of t...
Article
Full-text available
In this paper, we present the multilevel adaptive wavelet collocation method for solving non-divergent barotropic vorticity equation over spherical geodesic grid. This method is based on multi-dimensional second generation wavelet over a spherical geodesic grid. The method is more useful in capturing, identifying, and analyzing local structure [1]...
Article
Full-text available
We consider dynamical systems in which a (typically vectorvalued) dependentvariable evolves according to autonomousdynamics switching randomly according to Markovian laws that change with the value of the dependent variable. Such systems are known as “random evolutions” or, in electrical engineering contexts, as “switching systems”. Systems of this...

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Projects (3)
Project
The project aims to understand and develop new techniques on solving Linear system of Differential Equations.