Prof. Hao CHEN
Chongqing Normal University
In this talk, we consider a modified Douglas splitting method for a class of differential matrix equations, including differential Lyapunov and differential Riccati equations. The method we consider is based on a natural three-term splitting of the equations. The implementation of the algorithm requires only the solution of a linear algebraic system with multiple right-hand sides in each time step. It is proved that the method is convergent of order two and it preserves the symmetry and positive semidefiniteness of solutions of differential Lyapunov equations. Moreover, we show how the method can be handled in a low-rank setting for large-scale computations. We also provide a theoretical a priori error analysis for the low-rank algorithms. Numerical results are presented to verify the theoretical analysis.
Prof. Hao CHEN received his B.Sc. and Ph.D. from Huazhong University of Science and Technology in 2007 and 2012. His research interest is in “Numerical algorithms for partial differential equations, Numerical algorithms for integro-differential equations, numerical linear algebra, PDE constrained optimization”. He works as an Associate Professor at Chongqing Normal University.
Prof. Chen Hao is the member of the Professional Committee of Chinese Simulation Algorithms, Commentator of the American Mathematical Review. He has published more than 20 papers in international computational mathematics journals such as “J. Comput. Phys.”, “J. Sci. Comput.”, “BIT Numer. Math.”.