An algorithm and stability theory for downdating the ULV decomposition
type: Item
instance of: scholarly article
title: An algorithm and stability theory for downdating the ULV decomposition
zbMATH Open document ID: 0856.65042
DOI: 10.1007/BF01740542
author: Jesse L. Barlow
author: Peter A. Yoon
author: Hongyuan Zha
published in: BIT
publication date: 1997-02-24T00:00:00Z
review text: Special factorizations of \(A\in\mathbb{R}^{m \times n}\) \((m\geq n)\) of the form \(A=U {C\brack 0} V^T\) are considered, where \(U \in\mathbb{R}^{m \times m}\), \(V \in\mathbb{R}^{n \times n}\) are orthogonal, \(C \in R^{n\times n}\) is a lower triangular matrix. They serve as a means to separate the subspace associated with ``large'' and ``small'' singular values of \(A\). In some statistical problems it is desirable to delete a row from \(A\) and its factorized form (this is downdating). A special algorithm is suggested to preserve (in a sense) the structure in \(C\). A stability analysis is given with respect to round-off errors.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 881181
zbMATH Keywords: \(ULV\) decomposition
zbMATH Keywords: orthogonal decomposition
zbMATH Keywords: downdating
zbMATH Keywords: error analysis
zbMATH Keywords: singular values
zbMATH Keywords: algorithm
zbMATH Keywords: stability
reviewed by: Evgeniĭ Dyakonov
describes a project that uses: LINPACK
describes a project that uses: VanHuffel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 881181