D.V. Tiep, D.T.V. An, N.T.N. Oanh, N.T. Son, A generalized canonical metric for optimization on the indefinite Stiefel manifold, September 2025. accepted for publication in J. Optim. Theory Appl., February 2026.
N.T. Son, Brockett cost function for symplectic eigenvalues, June 2025.
D.V. Tiep, N.T. Son, A Riemannian optimization method on the indefinite Stiefel manifold, October 2024.
B. Gao, N.T. Son, T. Stykel, Symplectic Stiefel manifold: tractable metrics, second-order geometry, and Newton's methods, preprint, June 2024.
B. Gao, N.T. Son, T. Stykel, Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications, Linear Algebra and its Applications, 682: 50 - 85, 2024.
N.T. Son, T. Stykel, Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem, Electronic Journal of Linear Algebra, 38, 607-616, 2022.
N.T. Son, P.-A. Absil, B. Gao, T. Stykel, Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization SIAM Journal on Matrix Analysis and Applications, 42(4), 1732-1757, 2021.
B. Gao, N.T. Son, P.-A. Absil, T. Stykel, Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric, pp. 789 - 796 In: Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science, vol 12829. Springer, Cham.
B. Gao, N.T. Son, P.-A. Absil, T. Stykel, Riemannian Optimization on the Symplectic Stiefel Manifold, SIAM Journal on Optimization, 31(2), 1546-1575, 2021.
N.T. Son, P.-Y. Gousenbouger, E. Massart, T. Stykel, Balanced truncation for parametric linear systems using interpolation of Gramians: a comparison of algebraic and geometric approaches In: Benner P., Breiten T., Faßbender H., Hinze M., Stykel T., Zimmermann R. (eds) Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics, vol 171. Birkhäuser, pp. 31-51, 2021.
D.N. Hao, T.N.T. Quyen, N.T. Son, Convergence analysis of a Crank-Nicolson Galerkin method for an inverse source problem for parabolic systems with boundary observations, Applied Mathematics and Optimization, 84(2), 2289 - 2325, 2021.
N.T. Son, P.-Y. Gousenbourger, E. Massart, P.-A. Absil: Online balanced truncation for linear time-varying systems using continuously differentiable interpolation on Grassmann manifold, Proceedings of 6th International Conference on Control, Decision and Information Technologies, April 23-26, 2019, Paris, France (CoDIT'19), pp. 165 - 170
E. Massart, P.-Y. Gousenbourger, N.T. Son, T. Stykel, P.-A. Absil: Interpolation in the manifold of fixed-rank positive-semidefinite matrices for parametric model order reduction: preliminary results, Proceedings of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, April 24-26, 2019, Bruges, Belgium, (ESANN 2019), pp. 281-286
N.T. Son, T. Stykel: Solving parameter-dependent Lyapunov equations using the reduced basis method with application to parametric model order reduction, SIAM Journal on Matrix Analysis and Applications, 38(2), 479-504, 2017
N.T. Son, T. Stykel: Model order reduction of parameterized circuit equations based on interpolation, Advances in Computational Mathematics, 41(5), 1321-1342, 2015
N.T. Son: A real time procedure for parametric model order reduction using interpolation on Grassmann manifolds, International Journal for Numerical Methods in Engineering, 93(8), 818-833, 2013