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

About workshop: Tensor Computation and Machine Learning and Registration and Payment Link


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. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. J.K. Sahoo, P. Boggarapu, R. Behera and M. Z. Nashed. GD1 inverse and 1GD inverse for bounded operators on Banach spaces. accepted in Computational and Applied Mathematics. (June 2023)
  8. 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
  9. 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
  10. 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
  11. 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
  12. R. Behera, G. Maharana, and J. K. Sahoo Further results on weighted core-EP inverse of matricesResults in Mathematics, 75, 174 (2020). 
  13. B. Sitha, J. K. Sahoo, and R. Behera. Characterization of Weighted (b, c) Inverse of an Element in a Ring. Accepted in FILOMAT (2022)
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. J. K. Sahoo and R. Behera, Reverse-order law for core inverse of tensors. Computational and Applied Mathematics, 39(97), (2020).
  20. 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
  21. 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
  22. R. Behera, S. Meignen, and T. Oberlin,  Theoretical analysis of the second-order synchrosqueezing transform, Applied and Computational Harmonic Analysis, 45 (2018) 379-404.
  23. 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.
  24. 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.
  25. 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.
  26. R. Behera, and D. Mishra,  Further results on generalized inverses of tensors via Einstein product, Linear and Multilinear Algebra. 65(8) (2017) 1662-1682.
  27. 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.
  28. 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.
  29. 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.
  30. 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, R. R. Khilare, D. Gerontitis, P. Stanimirovic. Recurrent neural network for time varying tensor equations and its applications.
  2. S. K. Panda; J. K. Sahoo; R. Behera; P. S. Stanimirovic; D. Mosic; A. Stupina. The CEPGD-inverse for square matrices.
  3. B. Sitha; J. K. Sahoo; R. Behera; P. S. Stanimirovic; A. Stupina. Generalized core-EP inverse for square matrices.
  4. R. Behera, J. K. Sahoo, and R. N. Mohapatra. Characterization and Representation of Weighted Core Inverse of Matrices.
  5. R. Behera, J. K. Sahoo, R. N. Mohapatra and S. Das. Results on weak core inverse and central week core inverse.
  6. S. Santra, R. Behera. A novel higher-order numerical method for parabolic integro-fractional differential equations based on wavelets and $L2-1_\sigma$ scheme.

Projects

  • Project Title: Designing Algorithms for Tensor Decompositions and Inversions to Solve Multilinear Systems.
    Duration: Approved on December 2022 for 3-years.
    Funding Agency: Science and Engineering Research Board (SERB), Govt. of India
    Principal Investigator: Dr. Ratikanta Behera

  • Project Title: Efficient Algorithms for Solving Tensor Structure Equations and their Applications.
    Duration: June 2022 to June 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.
    Sanction on: June 2018 for 3-years.
    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.
    Sanction on: February 2018 for 3-years.
    Funding Agency: Science and Engineering Research Board (SERB), Govt. of India
    Principal Investigator: Dr. Ratikanta Behera




Current Students


      Biswarup Karmakar
      Ph. D. student (July 2022-Present)
      Email: biswarupk[at]isc.ac.in
      More details: CV

      Himanshu Pandey
      Ph. D. student (July 2022 -Present)
      Email: phimanshu[at]iisc.ac.in
      More details: CV

      AAAA BBBBB
      Ph. D. student (July 2023-Present)
      Email: AAABBB[at]isc.ac.in
      More details: CV

      Subhashree Patel
      Intern (Nov 2022 -Present)
      Email: Subhashreepatel[at]gmail.com
      More details: CV

      Sudarshan Santra
      Project Associate/Post-Doc (Oct 2022 -Present)
      Email: sudarshans[at]iisc.ac.in
      More details: Webpage

      Rushikesh Rajendra Khilare
      MTech student (May 2022 - May 2023)
      Email: rushikeshk[at]iisc.ac.in
      More details: CV

      Mohit Singhal
      MTech student (Aug 2022 - May 2024)
      Email: mohitsinghal[at]iisc.ac.in
      More details: CV

      Tarun Nayak
      MTech student (Aug 2022 - May 2024)
      Email: tarunnayak[at]iisc.ac.in
      More details: CV

      Mukul Mehar
      MTech student (Aug 2022 - May 2024)
      Email: mukulmehar[at]iisc.ac.in
      More details: CV


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 +91-317

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



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