Research

Research Interests

My research interest is in numerical algorithms. Currently, I am focusing on developing novel, efficient and reliable methods for algebraic eigenvalue, and eigenvalue related problems. Robust solvers for these problems are the backbone of present-day computations in scientific research and engineering.

Publications

Preprints

• Eigenvalue Backward Errors of Rosenbrock Systems and Optimization of Sums of Rayleigh Quotient
  with Anshul Prajapati, Punit Sharma, and Shreemayee Bora,
  technical report (submitted), 2024. (arXiv, MATLAB code)

Journal articles

• Locally Unitarily Invariantizable NEPv and Convergence Analysis of SCF
  with Ren-Cang Li,
  Math. Comp. 2024. 93: 2291–2329. (arXiv, MATLAB code)

• Variational characterization of monotone nonlinear eigenvector problems and geometry of self-consistent-field iteration
  with Zhaojun Bai,
  SIAM J. Matrix Anal. Appl., 2024. 45(1): 84-111. (arXiv, MATLAB code)

• Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems
  with Zhaojun Bai and Ren-Cang Li,
  SIAM J. Matrix Anal. Appl., 2022. 43(1): 301-327. (preprint, MATLAB code)

• Nonlinear eigenvector methods for convex minimization over the numerical range
  SIAM J. Matrix Anal. Appl., 2020. 41(4): 1771-1796. (paper)

• A globally convergent method to compute the real stability radius for time-delay systems
  with F. Borgioli, W. Michiels and Bart Vandereycken,
  Systems & Control Letters, volume 127, 2019. (paper)

• Robust Rayleigh quotient minimization and nonlinear eigenvalue problems
  with Zhaojun Bai and Bart Vandereycken,
  SIAM J. Sci. Comput., 2018. 40(5):A3495–A3522. (paper, MATLAB code)

• Subspace acceleration for the Crawford number and related eigenvalue optimization problems
  with Daniel Kressner and Bart Vandereycken,
  SIAM J. Matrix Anal. Appl., 2018. 39(2):961–982. (preprint, MATLAB code)

• Criss-cross type algorithms for computing the real pseudospectral abscissa
  with Bart Vandereycken,
  SIAM J. Matrix Anal. Appl., 2017. 38(3):891–923. (paper, RealPSPA package)

• Stability Analysis of the two-level orthogonal Arnoldi procedure
  with Yangfeng Su and Zhaojun Bai,
  SIAM J. Matrix Anal. Appl., 2016. 37(1): 195–214. (paper, MATLAB code)

• A Pade approximate linearization algorithm for solving the quadratic eigenvalue problem with low-rank damping
  with Xin Huang, Zhaojun Bai, and Yangfeng Su,
  Int. J. Numer. Methods Eng., 2015. 103(11): 840–858. (paper, PALM package)

Refereed conference papers

• Scalable Spectral Clustering with Group Fairness Constraints, with Ji Wang, Ian Davidson, and Zhaojun Bai, in the proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), pages 6613–6629, 2023. (arXiv)

• Matrix Powers Kernels for Thick-Restart Lanczos with Explicit External Deflation
  with Zhaojun Bai, J. Dongarra, and I. Yamazaki,
  in the proceedings of the 33th IEEE International Parallel and Distributed Processing Symposium (IPDPS), May 2019

Codes and Software

• uiNEPv: Locally Unitarily Invariantizable Nonlinear Eigenvector Problems. See details here.

• mNEPv: Monotone Nonlinear Eigenvector Problems. See details here.

• NEPvLib: A collection of benchmark instances for the Eigenvector-dependent Nonlinear Eigenvalue Problems (NEPv). See details here.

• RobustRQ: Robust Rayleigh quotient minimization by solving nonlinear eigenvalue problems (NEPv). See details here.

• RealPSPA: Criss-Cross methods for computing Real PseudoSpectral Abscissa. See details here.

• TOAR: A Two-level Orthogonal ARnoldi procedure to compute compact Arnoldi decomposition, and the orthogonal basis of second order Krylov subspace. See details here.

• PALM: A Pade Approximate Linearization Method to solve quadratic eigenvalue problems with low-rank damping matrix. See details here.