报告题目 (Title)：低秩逼近：列选主元随机 QR 算法及稀疏投影、高效低遍历相关技术
报告人 (Speaker)：冯月华 副教授（上海工程技术大学）
报告时间 (Time)：2026年1月15日（周四）10:30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：刘巧华
主办部门：理学院数学系
报告摘要：
In this talk, I will present improved algorithms for low-rank matrix approximation. Existing randomized methods—such as Randomized QR with Column Pivoting (RQRCP) and Flip-Flop spectrum-revealing QR (FFSRQR)—offer notable efficiency for large-scale problems but leave room for optimization. We first propose RQRCP-SEM, an enhanced RQRCP variant incorporating sparse projection via a sparse embedding matrix (SEM). Building on RQRCP-SEM and pass-efficient techniques, two pass-efficient FFSRQR-SEM variants are further developed to boost FFSRQR’s performance. Theoretical analyses of approximation error and computational complexity for these new algorithms are provided, with validation through numerical experiments.
