汇报标题 (Title)：Some new developments on Householder orthogonalization (Householder正交化的一些新进展)
汇报人 (Speaker)：邵美悦 教授（复旦大学）
汇报功夫 (Time)：2025年10月14日(周二) 16:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：刘巧华
主办部门：理学院数学系
汇报提要：
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.
