Currently research interests

Current research interests:
Perturbation theory for linear and nonlinear eigenvalue problems, Distance problems for matrices and matrix polynomials.
 

Research Projects:
Title: Distance Problems for Structured Matrix Polynomials.

Funding agencies: DST, India and DAAD, Germany under Project based Personal Exchange Programme, 2011.

Investigators: Shreemayee Bora, IIT Guwahati, (PI India), Christian Mehl, TU Berlin, (PI Germany), Michael Karow, TU Berlin, Punit Sharma, IIT Guwahati.

Period: 2011-2013.
Research Collaborators: Rafikul Alam, Volker Mehrmann, Michael Overton, Ralph Byers (deceased), Julio Moro, Christian Mehl, Michael Karow, Ravi Srivastava, Punit Sharma,  Madhu Belur, Ashish Kothyari

                                               

 

 Selected Publications:


  1. N. Roy, M. Karow, S. Bora & G. Armentia. Approximation of Pseudospectra of Block Upper Triangular Matrices. Linear Algebra and its Applications (accepted July, 2020).
  2. B. Das and S. Bora. Nearest Matrix Polynomials with Specified Elementary Divisors. SIAM Journal on Matrix Analysis and Applications (accepted in June, 2020).

  3. B. Das and S. Bora, Vector spaces of generalized linearizations for rectangular matrix polynomials. Electronic Journal of Linear Algebra, Vol. 35, 2019, pp 116-155. https://repository.uwyo.edu/ela/vol35/iss1/9

  4. A. Kothyari, B. Das, S. Bora and M. N. Belur, On the distance to nearest singular descriptor dynamical systems with impulsive initial conditions.  IEEE Transactions on Automatic Control, Vol. 64, (2019) No. 3, pp 1137-1149, DOI 10.1109/TAC.2018.2809741.

  5. S. Bora and R. Srivastava, Distance problems for Hermitian matrix pencils with eigenvalues of definite type. SIAM Journal on Matrix Analysis and Applications, Vol. 37, (2016) No. 1, pp.53-85.

  6. S. Bora and M. Karow, Structured Eigenvalue Perturbation Theory, P. Benner, M. Bollhofer, D. Kressner, C. Mehl and T. Stykel, editors, pp 199-222. Numerical Algebra, matrix Theory, Differential-Algebraic Equations and Control Theory (Festschrift in honor of V. Mehrmann), Springer, 2015.

  7. S. Bora,. M. Karow, C. Mehl and P. Sharma, Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures. SIAM Journal on Matrix Analysis and Applications, Vol. 36, (2015) No. 2, pp.393-416.

  8. S. Bora, M. Karow, C. Mehl and P. Sharma, Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures. SIAM Journal on Matrix Analysis and Applications, Vol 35, (2014) No. 2, pp. 453-475.

  9. R. Alam, S. Bora, M. Karow, V. Mehrmann and J. Moro. Perturbation theory for Hamiltonian matrices and the distance to bounded realness. SIAM Journal on Matrix Analysis and Applications, Vol 32,  (2011), No. 2,  pp.484-514.

  10. R. Alam, S. Bora, R. Byers and M. L. Overton. Characterization and construction of the nearest defective matrix via coalescence of pseudospectral components. Linear Algebra and its Applications, 435(2011),  pp. 494-513. [Cleve's Corner features this work] [Clever Moler's talk on this work in the Workshop on Advances in Numerical Linear Algebra, at the School of Mathematics, University of Manchester, May 29-30, 2019]                               

  11.  S. Bora. Structured eigenvalue condition number and backward error of a class of polynomial eigenvalue problems, SIAM Journal on Matrix Analysis and Applications, Vol 31,  (2009), No. 3, pp. 900-917.

  12. S. Bora and V. Mehrmann. Linear perturbation theory for structured matrix pencils arising in control theory, SIAM Journal on Matrix Analysis and Applications, Vol. 28(2006), No. 1, pp. 148-169.

  13. R. Alam and S. Bora. On sensitivity of eigenvalues and eigendecompositions of matrices, Linear Algebra and its Applications,   396(2005), pp. 273-301.

  14. R. Alam and S. Bora On stable eigendecompositions of matrices, SIAM Journal of Matrix Analysis and Applications, Vol. 26(2005), No. 3, pp. 830-848.
Selected conferences and research visits:

  1. FOCM, 2017, Barcelona, Spain, 10-19 July, 2017.

  2. 20th ILAS Conference, Leuven, Belgium, July 11-15, 2016.

  3. Workshop on 'Numerical Algebra, Matrix Theory, Differential Algebraic Equations and Control Theory (honoring Prof. V. Mehrmann on his 60th birthday), TU Berlin, Berlin Germany, May 6-9, 2015.

  4. Householder Symposium XIX, Spa, Belgium, June 8-13, 2014.

  5. Workshop on Numerical Linear Algebra and Optimization (honoring Prof. M. L. Overton on his 60th birthday), University of British Columbia, Vancouver, Canada, August 8-10, 2013.

  6. Research visit under project funded by DST, India, and DAAD, Germany, to TU Berlin, Germany during June 1-30, 2013.

  7. 18th Conference of the International Linear Algebra Society (ILAS), Providence, Rhode Island, USA, June 3-7, 2013.

  8. Research visit under project funded by DST, India, and DAAD, Germany, to TU Berlin, Germany during December 1-30, 2011.

  9. Householder Symposium XVIII, Lake Tahoe City, California, USA, June 12-17, 2011.

  10. International Conference on Industrial and Applied Mathematics (ICIAM08), Vancouver, Canada, July 18-22, 2011.

  11. 8th International Workshop on Accurate Solution of Eigenvalue Problems (IWASEP8), Berlin, Germany, June 28 - July 1, 2010.

  12. Householder Symposium XVII, Zeuthen, Germany, June 1-6, 2008.

  13. Research visit to ETH Zurich, Switzerland sponsored by ISBRI program of EPFL, Switzerland during May 15-30, 2008.

  14. Householder Symposium XV, Peebles, Scotland, June 17-21, 2002.
Research students:

  1. Ravi Srivastava. Ph.D. thesis titled 'Distance problems for Hermitian matrix polynomials - an epsilon pseudospectra based approach. (Graduated in 2012)

  2. Punit Sharma, PhD thesis titled 'Eigenvalue backward errors of polynomial eigenvalue problems under structure preserving perturbations. (Graduated in 2016)

  3. Biswajit Das (PhD work ongoing).

  4. Nandita Roy (PhD work ongoing).
Workshops and conferences organized:

  1. Advanced Instructional School on Numerical Linear Algebra at IIT Guwahati during December 1-22, 2010, fully funded by National Board for Higher Mathematics, India. (co-organized with Rafikul Alam)

  2. Advanced Training in Mathematics Workshop on Numerical Linear Algebra at IIT Guwahati during January 5-12, 2013, fully funded by the National Centre for Mathemaics, India. (co-organized with Rafikul Alam)

  3. International Conference on Numerical Linear Algebra and its Applications at IIT Guwahati during January 15-18, 2013. (co-organized with Rafikul Alam)

  4. Indian Women and Mathematics (IWM) regional workshop at IIT Guwahati during February 19-20, 2016.

  5. Minisymposium on 'Perturbation Theory and Distance Problems Associated with Eigenvalues' during 11-15 July, 2016 at the 20th ILAS Conference, Leuven, Belgium. (co-organized with Christian Mehl)
 

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