Connecting randomized iterative methods with Krylov subspaces

发布时间：2025-07-04 作者：浏览次数：

Speaker:	谢家新	DateTime:	2025年7月4日（周五）下午14:00-15:30
Brief Introduction to Speaker: 谢家新，副教授，北京航空航天大学		Place:	国交2号楼315会议室
Abstract:Randomized iterative methods, such as the randomized Kaczmarz method, have gained significant attention for solving large-scale linear systems due to their simplicity and efficiency. Meanwhile, Krylov subspace methods have emerged as a powerful class of algorithms, known for their robust theoretical foundations and rapid convergence properties. Despite the individual successes of these two paradigms, their underlying connection has remained largely unexplored. In this talk, we develop a unified framework that bridges randomized iterative methods and Krylov subspace techniques, supported by both rigorous theoretical analysis and practical implementation. The core idea is to formulate each iteration as an adaptively weighted linear combination of the sketched normal vector and previous iterates, with the weights optimally determined via a projection-based mechanism. This formulation not only reveals how subspace techniques can enhance the efficiency of randomized iterative methods, bu...