j9九游会

报告问题 (Title)：Some new developments on Householder orthogonalization (Householder正交化的一些新希望)

报告人 (Speaker)：邵美悦 教授（复旦大学）

报告时间 (Time)：2025年10月14日(周二) 16:00

报告所在 (Place)：校本部GJ303

约请人(Inviter)：刘巧华

主理部分：理学院数学系

报告摘要：

Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning of the input vectors. However, there are a few issues that have limited the use of Householder orthogonalization. For example, the classical Householder orthogonalization algorithm is only applicable in the standard inner product, and is difficult to apply in the context of a nonstandard inner product. Another case that is frequently encountered in eigenvalue problems is the orthogonalization of a set of vectors against an existing orthogonal basis. Most algorithms for this problem in the literature are based on block Gram–Schmidt orthogonalization, and Householder orthogonalization is rarely studied. We propose solutions to these problems so that the use of Householder orthogonalization is greatly expanded. Theoretical analysis and numerical experiments demonstrate that our approaches are numerically stable under mild assumptions.