邵年 博士（洛桑联邦理工学院）

郑伟英 研究员

Stabilizing the Rayleigh--Ritz Procedure by Randomization

7月31日（周五）10:00-11:00，南楼202

Extracting approximate eigenpairs from a prescribed subspace is of fundamental importance in eigenvalue computation. While projecting the target eigenvector onto the subspace yields satisfactory accuracy, extracting an approximate eigenpair that attains a comparable convergence rate has remained a long-standing open problem. Although the standard Rayleigh--Ritz procedure is widely used for this purpose, it may suffer from deteriorated convergence of Ritz values and may even fail to produce convergent Ritz vectors. In this talk, we address this long-standing open problem by introducing a randomized Rayleigh--Ritz procedure whose output converges at a rate similar to the ideal projection. Our analysis requires only the simplicity of the target eigenvalue and extends naturally to nonlinear eigenvalue problems.