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Numerical Algorithms and Tensor Learning Laboratory

Numerical Algorithms and Tensor Learning Laboratory

Dr. Ratikanta Behera

Dr. Ratikanta Behera

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Journal Publications

2025

• H. Pandey, A. Singh, R. Behera. An efficient wavelet-based physics-informed neural networks for singularly perturbed problems.  Neurocomputing (Submitted).


• S. Santra, R. Behera. Enhancing accuracy with an adaptive discretization for the non-local integro-partial differential equations involving initial time singularities. Computers and Mathematics with Applications. (Submitted)


• R. Behera, K. Panigrahy, J. K. Sahoo, and Y. Wei. M-QR decomposition and hyperpower iterative methods for computing outer inverses of tensors. Journal of Computational and Applied Mathematics. (Submitted)


• S. Patel, S. Santra, R. Behera. A hybrid numerical method for time-delayed fractional sub-diffusion equations with multi-singularities. Numerical Algorithms. (Submitted)


• K. Panigrahy, B. Karmakar, J. K. Sahoo, R. Behera, and R. N. Mohapatra. Computation of $M$-QDR decomposition of tensors and applications.  Accepted for publication in Journal of Applied Mathematics and Computing.


• B. Sitha, R. Behera, J. K. Sahoo, R. N. Mohapatra, P. S. Stanimirovic, and Alena Stupina. Characterizations of Weighted Generalized Inverses.  Aequationes mathematicae (2025)



2024

• R. Behera, J. K. Sahoo, and Y. Wei. Computation of outer inverse of tensors based on $t$-product.  Numerical Linear Algebra with Applications Accepted (2024).


• J. K. Sahoo, S. K. Panda, R. Behera, P. Stanimirovic. Computations of Tensors Generalized Inverses under M-Product and Applications.  Journal of Mathematical Analysis and Applications (2024).


• S. Santra, R. Behera. Simultaneous space-time Hermite wavelet framework for time-fractional nonlinear weakly singular integro-partial differential equations.  Communications in Nonlinear Science and Numerical Simulation (2024).


• R. Behera, J. K. Sahoo, P. S. Stanimirovic, A. Stupina, A. Stupin. Computing Tensor Generalized bilateral inverses. Communications on Applied Mathematics and Computation (2024).



2023

• R. Behera, D. Gerontitis, P. Stanimirovic, V. Katsikis, Y. Shi, Xinwei Cao. An Efficient Zeroing Neural Network for Solving Time-Varying Nonlinear Equations. Neural Computing and Applications (2023). https://doi.org/10.1007/s00521-023-08621-x


• B. Sitha; J. K. Sahoo; R. Behera; P. S. Stanimirovic; A. Stupina. Generalized core-EP inverse for square matrices. Computational and Applied Mathematics (2023). https://www.springer.com/journal/40314


• J.K. Sahoo, P. Boggarapu, R. Behera and M. Z. Nashed. GD1 inverse and 1GD inverse for bounded operators on Banach spaces. Computational and Applied Mathematics (June 2023)


• S. K. Panda; J. K. Sahoo; R. Behera; P. S. Stanimirovic; D. Mosic; A. A. Stupina. The CEPGD-inverse for square matrices. Bulletin of the Iranian Mathematical Society (2023). https://doi.org/10.1007/s41980-022-00715-x


• P. K. Sahu, K. S. Patel and R. Behera Three-time levels compact scheme for pricing European options under regime switching jump-diffusion models. Proceedings of the Ninth International Conference on Mathematics and Computing. ICMC 2023 2023. Lecture Notes in Networks and Systems, vol 697. Springer, Singapore. https://doi.org/10.1007/s00521-023-08621-x


• P. Stanimirovic, D. Mosic, A. Stupina, R. Behera. Solving matrix approximation problems using generalized inverses. Moscow: INFRA-M, 2023. - 165 p. - (Scientific Idea). ISBN 978-5-16-019628-2.





2022

• D. Gerontitis, R. Behera, Y. Shi, P. S. Stanimirovic. A Robust Noise Tolerant Zeroing Neural Network for Solving Time-Varying Linear Matrix Equations. Neurocomputing (2022) https://doi.org/10.1016/j.neucom.2022.08.036


• D. Gerontitis,  R. Behera,  P. Tzekis, P. Stanimirovic.  A Family of Varying-Parameter Finite-Time Recurrent Neural Networks for Time-Varying Sylvester Equation and its Application. Journal of Computational and Applied Mathematics. 403, (2022), 113826. https://doi.org/10.1016/j.cam.2021.113826


• R. Behera, G. Maharana, J. K. Sahoo, P. S. Stanimirovic. Characterizations of the Weighted Core-EP Inverses. Bulletin of the Iranian Mathematical Society (2022). https://doi.org/10.1007/s41980-022-00715-x


• B. Sitha, J. K. Sahoo, and R. Behera. Characterization of Weighted (b, c) Inverse of an Element in a Ring. FILOMAT 36, 14 (2022)


• S. Das, J. K. Sahoo, and R. Behera. Further results on weighted core inverse in a ring. Linear and Multilinear Algebra. 2022. https://doi.org/10.1080/03081087.2022.2128023



2013 - 2021

• D. Gerontitis, R. Behera, J. K. Sahoo, P. Stanimirovic.  Improved finite-time zeroing neural network for time-varying division. Studies in Applied Mathematics, 2021; 146: 526-549. https://doi.org/10.1111/sapm.12354


• R. Behera, J. K. Sahoo, R. N. Mohapatra, and M. Z. Nashed. Computation of Generalized Inverses of Tensors via t-Product. Numerical Linear Algebra with Applications (2021). https://doi.org/10.1002/nla.2416


• P.  Stanimirovic,  D. Gerontitis,  P. Tzekis   R. Behera,  J. K. Sahoo.  Simulation of Varying Parameter Recurrent Neural Network with application to matrix inversion. Mathematics and Computers in Simulation (2021). https://doi.org/10.1016/j.matcom.2021.01.018


• P. S. Stanimirovic,  J. R. Sendra,  R. Behera,  J. K. Sahoo,  D. Mosic;  J. Sendra,  A. Lastra.  Computing tensor generalized inverses via specialization and rationalization. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas. (2021)   https://doi.org/10.1007/s13398-021-01057-9


• D. Mosic, P. S. Stanimirovic, J. K. Sahoo, R. Behera, and V. N. Katsikis. One-sided weighted outer inverses of tensors. Journal of Computational and Applied Mathematics (2021) 113293, https://doi.org/10.1016/j.cam.2020.113293


• R. Behera, G. Maharana, and J. K. Sahoo Further results on weighted core-EP inverse of matrices.  Results in Mathematics, 75, 174 (2020). 


• R. Behera,  D. Mosic,  J. K. Sahoo, and  P. S. Stanimirovic. Weighted Inner Inverse for Rectangular Matrices, Quaestiones Mathematicae, (2020), https://doi.org/10.2989/16073606.2020.1836688


• R. Behera, S. Maji, and R. N. Mohapatra. Weighted Moore-Penrose inverses of arbitrary-order tensors. Computational and Applied Mathematics. 39, 284, (2020), https://doi.org/10.1007/s40314-020-01328-y


• R. Behera, A. K. Nandi, and J. K. Sahoo, Further results on the Drazin inverse of even-order tensors. Numerical Linear Algebra with Applications (2020) https://doi.org/10.1002/nla.2317


• J. K. Sahoo, R. Behera, P. S. Stanimirovic and V. N. Katsikis. Computation of outer inverses of tensors using the QR decomposition. Computational and Applied Mathematics. (2020) https://doi.org/10.1007/s40314-020-01225-4


• R. Behera and J. K. Sahoo, Generalized Inverses of Boolean Tensors via Einstein Product,  Linear and Multilinear Algebra (2020), https://doi.org/10.1080/03081087.2020.1737630


• J. K. Sahoo and R. Behera, Reverse-order law for core inverse of tensors. Computational and Applied Mathematics, 39(97), (2020).


• J. K. Sahoo, R. Behera, P. S. Stanimirovic, V. N. Katsikis, and H. Ma. Core and Core-EP Inverses of Tensors. Computational and Applied Mathematics, (2020). https://doi.org/10.1007/s40314-019-0983-5


• K. Panigrahy, R. Behera, and D. Mishra, Reverse order law for the Moore-Penrose inverses of tensors, Linear and Multilinear Algebra,  68(2), 2020, 246-264


• R. Behera, S. Meignen, and T. Oberlin, Theoretical analysis of the second-order synchrosqueezing transform, Applied and Computational Harmonic Analysis, 45 (2018) 379-404.


• R. Maulik, O. San, and R. Behera, An adaptive multilevel wavelet framework for scale-selective WENO reconstruction schemes, International Journal for Numerical Methods in Fluids, 87(5) (2018) 239-269.


• R. Behera, and M. Mehra, An adaptive wavelet collocation method for solution of the convection dominated problem on the sphere, International Journal of Computational Methods, 15(1) (2018) 1850080-1850098.


• R. Behera and M. Mehra, Approximation of the differential operators on an adaptive spherical geodesic grid using spherical wavelet, Mathematics and Computers in Simulation, 132 (2017) 120-138.


• R. Behera, and D. Mishra, Further results on generalized inverses of tensors via Einstein product, Linear and Multilinear Algebra. 65(8) (2017) 1662-1682.


• R. Behera, M. Mehra and N. K. R. Kevlahan, Multilevel Approximation of the Gradient Operator on an Adaptive Spherical Geodesic Grid, Advances in Computational Mathematics, 41(3) (2015) 663-689.


• R. Behera and M. Mehra, A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation, Journal of Multiscale Modelling, 06 (1) (2015) 1450001-1430023.


• R. Behera and M. Mehra, Integration of Barotropic Vorticity Equation Over Spherical Geodesic Grid using Multilevel Adaptive Wavelet Collocation Method, Applied Mathematical Modelling, 37 (2013) 5215-5226.


• R. Behera and M. Mehra,  Approximate solution of Modified Camassa-Holm and Degasperis-Procesi Equations using Wavelet optimized finite difference method, Int. J. Wavelets Multiresolut. Inf. Process.11 (2013) 1350019.

Preprints / Communicated / Under preparation Articles

• P. Stanimirovic, M. Ciric, D. Gerontitis, S. Mourtas, R. Behera. Neural dynamics for computing approximate bisimulations for weighted finite automata over the field of real numbers.


• R. Behera, S. K. Panda, J. K. Sahoo. Two-step parameterized tensor-based iterative methods for solving AXB=C.


• R. Raj, A. Srivastava, R. Behera. Automation - Augmentation of Artificial Intelligence and Human Intelligence.


• B. Karmakar, R. Behera. Efficient iterative methods for computing generalized inverse of tensors based on $t$-product


• B. Karmakar, R. Behera. Robust low-rank tensor completion via nonconvex weighted correlated total variation and sparse regularization


• N. Bhadala and R. Behera. Generalized inverses of the quaternion matrices with applications.


• S. Santra, R. Behera. Space-time wavelet collocation method for integro-differential equations in RLC circuits and viscoelastic models with non-local operators.


• S. Santra, R. Behera. Wavelet-based $L2-1_\sigma$ approach for time-fractional option pricing model under jump-diffusion.


• R. Behera, R. R. Khilare, D. Gerontitis, P. Stanimirovic. Recurrent neural network for time varying tensor equations and its applications.


• R. Behera, J. K. Sahoo, R. N. Mohapatra, S. Das, S. K. Prajapati. Results on weak core inverse and central week core inverse.