»ã±¨±êÌâ (Title)£ºSome new developments on Householder orthogonalization (HouseholderÕý½»»¯µÄһЩнøÕ¹)

»ã±¨ÈË (Speaker)£ºÉÛÃÀÔà ½ÌÊÚ£¨¸´µ©´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê10ÔÂ14ÈÕ(Öܶþ) 16:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

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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¨CSchmidt 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.