讲座主题：TriCG with deflated restarting for symmetric quasi-definite linear systems

专家姓名：杜魁

工作单位：厦门大学

讲座时间：2026年10月20日 08:30-09:30

讲座地点：腾讯会议：202-293-760

主办单位：烟台大学数学与信息科学学院

内容摘要：

TriCG is a short-recurrence iterative method recently introduced by Montoison and Orban [SIAM J. Sci.\ Comput., 43 (2021), pp. A2502-A2525] for solving symmetric quasi-definite (SQD) linear systems. TriCG takes advantage of the inherent block structure of SQD linear systems and performs substantially better than SYMMLQ. However, numerical experiments have revealed that the convergence of TriCG is typically slow when the off-diagonal block contains a substantial number of large elliptic singular values. To address this limitation, we introduce a deflation strategy tailored for TriCG to improve its convergence behavior. Specifically, we develop a generalized Saunders-Simon-Yip process with deflated restarting to construct the deflation subspaces. Building upon this process, we propose a novel method termed TriCG with deflated restarting. The deflation subspaces can also be utilized to solve SQD linear systems with multiple right-hand sides. Numerical experiments are provided to illustrate the superior performance of the proposed methods.

主讲人介绍：

杜魁，厦门大学数学科学学院教授、博导，2009年8月博士毕业于香港城市大学，2009年9月至2011年4月在芬兰阿尔托大学做博士后，2011年6月至今在厦门大学数学科学学院工作；主持国家自然科学基金面上项目三项，参与重大研究计划重点支持项目一项；目前主要研究兴趣为大规模线性方程组Krylov子空间方法、随机迭代法，反问题的计算方法等。