报告题目：Projection Methods and Inheritance Properties for Large-Scale Sylvester Equations

报告人：朱景华(Eric King-wah Chu) 教授

报告人单位：澳大利亚莫纳什大学(Monash University)

报告时间：2026年11月5日, 下午4：30-5：30

报告地点：国产自拍 数学科学学院 301

报告摘要： In this talk, we consider the numerical solution of large-scale nonsingular Sylvester equations of the form (or the generalized form ), where the spectra and (or and for the generalized version) are disjoint. Under a stability assumption, we construct rational Krylov subspaces, inspired by the deflating subspaces for matrix pencils. These subspaces are further extended to handle generalized Sylvester equations, yielding new Krylov subspaces tailored for the Petrov-Galerkin projection method. Using these subspaces, the Sylvester equation is projected to a smaller Sylvester equation, which is easier to solve. We would like to explore the inheritance properties of such projection methods — what nice properties of the original Sylvester equation are passed onto the projected equation. We consider solvability (in terms of the separation of spectra and perturbation), as well as the stability of the defining matrices or pencils. These will form a firmer basis for the applicability of projection methods. Some illustrative numerical examples are provided.

报告人简介：

Eric King-wah Chu(朱景华)为世界百强名校澳大利亚莫纳什大学（Monash University）国产自拍 教授。1976年于香港中文大学数学系获得学士学位，1978和1981年于英国的巴斯大学（University of Bath）数学系先后获得硕士学位和博士学位。主要研究领域涉及科学计算，数值分析，控制论，最优化以及积分方程等。先后访问过加拿大的卡尔加里大学，滑铁卢大学，美国北伊利诺爱大学，英国牛津大学，新加坡国立大学，香港城市大学，台湾清华大学，台湾师范大学，北京大学，复旦大学等高校。已在国际重要学术期刊SIAM J. Sci. Comput.，SIAM J. Numer. Anal.，SIMA J.Matrix Anal. Appl.，IEEE Trans. Automat. Control，Numer. Math.，Numer. Linear Algebra Appl.，Linear Algebra Appl.，J. Comput. Appl. Math.等发表SCI学术论文80余篇。现担任国际重要杂志SIAM Journal on Matrix Analysis and Applications副主编。