Current Research Interests

Numerical Linear Algebra, Linear/Nonlinear Eigenvalue Problems, Numerical Solution of Ordinary Differential Equations, Reduced Order Modeling, High Performance Computing, Optimization on Manifolds, Machine Mining, System Support for Scientific Computations, Elementary Function Computations, IEEE Floating Point Arithmetics.

 

 

Selected Publications

• Liu, C., Wang, W.-G., Xue, J., Li, R.-C.
  Accurate numerical solution for structured M-matrix algebraic Riccati equations
  (2021) Journal of Computational and Applied Mathematics, 396, art. no. 113614, .
  
• Truhar, N., Li, R.-C.
  On an eigenvector-dependent nonlinear eigenvalue problem from the perspective of relative perturbation theory
  (2021) Journal of Computational and Applied Mathematics, 395, art. no. 113596, .
  
• Liu, F., Wang, L., Lou, Y., Li, R.-C., Purdon, P.L.
  Probabilistic Structure Learning for EEG/MEG Source Imaging with Hierarchical Graph Priors
  (2021) IEEE Transactions on Medical Imaging, 40 (1), art. no. 9201541, pp. 321-334.
  
• Wang, L., Zhang, L.-H., Bai, Z., Li, R.-C.
  Orthogonal canonical correlation analysis and applications
  (2020) Optimization Methods and Software, 35 (4), pp. 787-807.
  
• Liu, C., Xue, J., Li, R.-C.
  Accurate Numerical Solution for Shifted M-Matrix Algebraic Riccati Equations
  (2020) Journal of Scientific Computing, 84 (1), art. no. 15, .
  
• Truhar, N., Tomljanović, Z., Li, R.-C.
  Perturbation theory for Hermitian quadratic eigenvalue problem – damped and simultaneously diagonalizable systems
  (2020) Applied Mathematics and Computation, 371, art. no. 124921, .
  
• Wang, L., Li, R.-C.
  Learning Low-Dimensional Latent Graph Structures: A Density Estimation Approach
  (2020) IEEE Transactions on Neural Networks and Learning Systems, 31 (4), art. no. 8738989, pp. 1098-1112.
  
• Wang, L., Li, R.
  A Scalable Algorithm for Large-scale Unsupervised Multi-view Partial Least Squares
  (2020) IEEE Transactions on Big Data, .
  
• Greenbaum, A., Li, R.-C., Overton, M.L.
  First-order perturbation theory for eigenvalues and eigenvectors
  (2020) SIAM Review, 62 (2), pp. 463-482.
  
• Chen, C., Li, R.-C., Ma, C.
  Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process
  (2019) Linear Algebra and Its Applications, 583, pp. 1-45.
  
• Cai, Y., Li, R.-C.
  Perturbation analysis for matrix joint block diagonalization
  (2019) Linear Algebra and Its Applications, 581, pp. 163-197.
  
• Wang, X., Li, X., Zhang, L.-H., Li, R.-C.
  An Efficient Numerical Method for the Symmetric Positive Definite Second-Order Cone Linear Complementarity Problem
  (2019) Journal of Scientific Computing, 79 (3), pp. 1608-1629.
  
• Liu, C., Li, R.-C.
  Structured backward error for palindromic polynomial eigenvalue problems, II: Approximate eigentriplets
  (2018) Frontiers of Mathematics in China, 13 (6), pp. 1397-1426.
  
• Song, Z., Baxter, M., Jin, M., Wang, J.-X., Li, R.-C., Johnson, T., Su, J.
  Sparse sampling and fully-3D fast total variation based imaging reconstruction for chemical shift imaging in magnetic resonance spectroscopy
  (2018) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 11309 LNAI, pp. 479-485.
  
• Cai, Y., Zhang, L.-H., Bai, Z., Li, R.-C.
  On an eigenvector-dependent nonlinear eigenvalue problem
  (2018) SIAM Journal on Matrix Analysis and Applications, 39 (3), pp. 1360-1382.