Dr. Ratikanta Behera
Assistant Professor
Department of Computational and Data Sciences,
Indian Institute of Science, Bangalore, India

Research Areas

  • Tensor Decompositions, Neural Networks, Numerical Linear Algebra, Generalized Inverses of Tensors, Wavelets in Scientific Computing, High-Performance Computing.

About my Research: Numerical Algorithms and Tensor Learning Lab


Research Experience

  • Assistant Professor (May-2022 to ---)
    Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India
  • Postdoctoral Researcher (December-2019 to May-2022)
    Department of Mathematics, University of Central Florida, Orlando, USA
  • Assistant Professor (July-2016 to December-2019),
    Department of Mathematics and Statistics, IISER Kolkata, India.
  • Postdoctoral Research (Jan-2015 to July-2016),
    Laboratoire Jean Kuntzmann (LJK), Joseph Fourier University, Grenoble, France.
  • Postdoctoral Researcher, (Dec-2013 to Dec-2014),
    Department of Aerospace and Mechanical engineering, University of Notre Dame, South Bend, USA.
  • Ph.D. Mathematics (2013),
    Indian Institute of Technology (IIT) Delhi, New Delhi, India.

Other Profiles

Journal Publications

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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, FĂ­sicas y Naturales. Serie A. Matematicas.  https://doi.org/10.1007/s13398-021-01057-9
  8. 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
  9. D. Gerontitis, R. Behera, J. K. Sahoo, P. Stanimirovic.  Improved finite-time zeroing neural network for time-varying division. Studies in Applied Mathematics, 2021146526-549. https://doi.org/10.1111/sapm.12354
  10. R. Behera, G. Maharana, and J. K. Sahoo Further results on weighted core-EP inverse of matricesResults in Mathematics, 75, 174 (2020). 
  11. B. Sitha, J. K. Sahoo, and R. Behera. Characterization of Weighted (b, c) Inverse of an Element in a Ring. Accepted in FILOMAT (2022)
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. J. K. Sahoo and R. Behera, Reverse-order law for core inverse of tensors. Computational and Applied Mathematics, 39(97), (2020).
  18. 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
  19. 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
  20. R. Behera, S. Meignen, and T. Oberlin,  Theoretical analysis of the second-order synchrosqueezing transform, Applied and Computational Harmonic Analysis, 45 (2018) 379-404.
  21. 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.
  22. 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.
  23. 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.
  24. R. Behera, and D. Mishra,  Further results on generalized inverses of tensors via Einstein product, Linear and Multilinear Algebra. 65(8) (2017) 1662-1682.
  25. 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.
  26. 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.
  27. 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.
  28. 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.


Submitted to Journal

  1. R. Behera, D. Gerontitis, P. Stanimirovic, V. Katsikis, Y. Shi. Varying Parameter Improved Zeroing Neural Networks for Solving Nonlinear Equations
  2. R. Behera, J. K. Sahoo, and R. N. Mohapatra. Characterization and Representation of Weighted Core Inverse of Matrices.
  3. J. K. Sahoo, R. Behera, R. N. Mohapatra and S. Das. Weak core and central weak core inverses.
  4. J.K. Sahoo, P. Boggarapu, R. Behera and M. Z. Nashed. GD1 inverse and 1GD inverse for Hilbert space operators

Projects

  • Project Title: Designing Algorithms for Tensor Decompositions and Inversions to Solve Multilinear Systems.
    Duration:
    Funding Agency:
    Principal Investigator: Dr. Ratikanta Behera

  • Project Title: Efficient Algorithms for Solving Tensor Structure Equations and their Applications.
    Duration: July 2022 to July 2024.
    Funding Agency: IISc Bangalore
    Principal Investigator: Dr. Ratikanta Behera

  • Project Title: A dynamically adaptive wavelet algorithm for solution of evolution equations with localized structures.
    Duration: June 2018 to December 2019.
    Funding Agency: Science and Engineering Research Board (SERB), Govt. of India
    Principal Investigator: Dr. Ratikanta Behera

  • Project Title: Tensor-valued wavelet analysis and application to solution of differential equations.
    Duration: February 2018 to December 2019
    Funding Agency: Science and Engineering Research Board (SERB), Govt. of India
    Principal Investigator: Dr. Ratikanta Behera

Current Students


Mr. Himanshu Pandey
Email: phimanshu@iisc.ac.in
PhD Student
Join on: July 2022
Mr. Biswarup Karmakar
Email: biswarupk7@gmail.com
PhD Student
Join on: July 2022

Mr. Rushikesh Rajendra Khilare
Email: rushikeshk@iisc.ac.in
M. Tech Student
Join on: May 2022
Mr. Sudarshan Santra
Email: sudarshans@iisc.ac.in
Research Associate
Join on: October 2022


Ms. Subhashree Patel
Email: subhashree@iisc.ac.in
Intern
Join on: November 2022

Reviewer in International Journals

  • IEEE Transactions on Signal Processing
  • Linear and Multilinear Algebra
  • Applied Mathematics and Computation
  • Bulletin of the Iranian Mathematical Society
  • Journal of Applied Mathematics and Computing
  • Journal of Computational and Applied Mathematics
  • Advances in Applied Clifford Algebras
  • American Mathematical Society (AMS) mathematical review
  • Acta Applicandae Mathematicae
  • International Journal of Modern Physics C
  • Special Matrices
  • Numerical Functional Analysis and Optimization

Teaching

Email or Call at +91 9310192034

Room Number- 317
Department of Computational and Data Sciences,
Indian Institute of Science
Bangalore, India 560012
Fax: +91 9310192034



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