邵年 博士（洛桑联邦理工学院）

郑伟英 研究员

Fast and Stable Randomized Methods for Large-Scale Eigenvalue Problems

7月31日（周五）9:00-10:00，南楼202

Randomization has become an increasingly powerful tool in numerical linear algebra, often yielding surprisingly simple algorithms that outperform traditional deterministic methods. The poster child of these developments, the randomized SVD, is now one of the state-of-the-art approaches for performing low-rank approximation. Moving beyond the randomized SVD, this talk illustrates how randomness inspires novel solutions for notoriously difficult problems, with a specific focus on eigenvalue problems. We examine this paradigm by addressing high-dimensional null space computation, fast orthogonalization in Krylov subspaces, reliable eigenpair extraction, and resolvent-based nonlinear eigensolvers. A common theme of these developments is that randomization helps to transform linear algebra results that only hold generically into robust and reliable numerical algorithms.