# Xiaobo Liu

Welcome to my webpage. I am currently a postdoctoral researcher in the Computational Methods in Systems and Control Theory (CSC) group at the Max Planck Institute for Dynamics of Complex Technical Systems (MPI-DCTS) in Magdeburg, Germany, working with Prof. Peter Benner.

Prior to moving to Magdeburg, I was a research associate in the Numerical Linear Algebra Group (NLA Group) at The University of Manchester, working with Prof. Nicholas J. Higham. I completed my PhD (Sep 2018-Jun 2022) in the Department of Mathematics at The University of Manchester under the supervision of Prof. Nicholas J. Higham and Prof. Françoise Tisseur.

My main research interests are in Numerical Analysis and Numerical Linear Algebra, including the design, development, and analysis of numerical algorithms (possibly) utilizing mixed-precision arithmetic. I have particularly focused on computing polynomials and functions of matrices and solving Sylvester equations, but I have been keen to broaden my research horizons and study other important kernels in scientific computing, such as linear systems, least squares problems, and matrix factorizations. One of my current focuses is to utilize multiple precisions to accelerate the process of solving matrix equations such as the algebraic Riccati equations.

## News

**Jan 1, 2024:** I finished my contract in the NLA Group at The University of Manchester and joined the CSC group at MPI-DCTS to work with Prof. Peter Benner.

**Dec 27, 2023:** New preprint: Mixed-precision Paterson–Stockmeyer method for evaluating polynomials of matrices.

**Aug 22, 2023:** I gave a talk on Mixed-precision Paterson–Stockmeyer method for evaluating matrix polynomials at ICIAM 2023.

**Jun 28, 2023:** I gave a talk in the minisymposium Approximate Computing in Numerical Linear Algebra organized by Prof. Nicholas J. Higham, Dr. Bastien Vieublé and myself at the 29th Biennial Numerical Analysis Conference.

## Preprints

▪ Mixed-precision Paterson–Stockmeyer method for evaluating polynomials of matrices, preprint, https://arxiv.org/abs/2312.17396.

▪ On the cross-shaped matrices. MIMS EPrint 2023.1, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, January 2023.

## Journal Articles

▪ Computing the square root of a low-rank perturbation of the scaled identity matrix (with M. Fasi and N. J. Higham). SIAM J. Matrix Anal. Appl., 44(1):156-174, 2023.

▪ Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative (with A. H. Al-Mohy and N. J. Higham). SIAM J. Matrix Anal. Appl., 43(1):233-256, 2022.

▪ A multiprecision derivative-free Schur-Parlett algorithm for computing matrix functions (with N. J. Higham). SIAM J. Matrix Anal. Appl., 42(3):1401-1422, 2021.

## Thesis

▪ Computing matrix functions in arbitrary precision arithmetic, doctoral thesis, Department of Mathematics, The University of Manchester, Manchester, UK, June 2022.

## Previous Teaching

▪ 2021/22 S2 MATH10242 Sequences and Series, MATH36022 Numerical Analysis II

▪ 2021/22 S1 MATH20701 Probability II, MATH36001 Matrix Analysis

▪ 2020/21 S2 MATH10212 Linear Algebra B

▪ 2020/21 S1 MATH10131 Calculus and Vectors B, MATH36061 Convex Optimization

▪ 2019/20 S2 MATH20602 Numerical Analysis I, MATH36022 Numerical Analysis II

▪ 2019/20 S1 MATH19661 Mathematics for MACE, MATH19681 Mathematics for EEE

▪ 2018/19 S2 MATH10222 Calculus and Applications A, MATH36022 Numerical Analysis II

▪ 2018/19 S1 MATH20401 PDEs and Vector Calculus A

## Links

▪ Nick Higham’s blog on applied mathematics, software and workflow.

▪ I was a committee member of Manchester SIAM-IMA Student Chapter from 2018 to 2022.

## Contact details

Office S3.11, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germany

Phone: +49 391 6110 381 Email: xliu[at]mpi-magdeburg.mpg.de

_{ Last updated Jan 2024. }