Xiaobo Liu, Doctor

Bastien Vieuble, Doctor

Mixed-Precision Algorithms for Solving Linear Matrix Equations

15:00-16:00 September 7 (Monday), N202

Mixed precision has become an increasingly popular strategy in numerical linear algebra and scientific computing. It performs most computations in low-precision arithmetic while selectively using higher precision to maintain the required accuracy, thereby improving performance relative to uniform-precision methods. One successful realization of this principle is mixed-precision iterative refinement (MPIR). In this talk, we present MPIR approaches for accelerating the solution of Sylvester equations and low-rank Lyapunov equations. Separate computational frameworks are discussed for the two classes of matrix equations. We provide rounding-error and computational-cost analyses and present numerical experiments demonstrating the accuracy and efficiency of the proposed methods.

Bio: Xiaobo Liu is a postdoctoral researcher in the Computational Methods in Systems and Control Theory group at the Max Planck Institute for Dynamics of Complex Technical Systems, led by Prof. Peter Benner. Previously, he was a research associate in the Numerical Linear Algebra Group at the University of Manchester, where he also completed his PhD in 2022 under the supervision of Prof. Nicholas J. Higham. His research focuses on the design, analysis, and development of algorithms in numerical linear algebra. During his PhD, he studied the computation of matrix functions in arbitrary precision arithmetic, while part of his recent work has focused on mixed-precision computation.