An algorithm and a stability theory for downdating the ULV decomposition

Jesse Louis Barlow, Peter A. Yoon, Hongyuan Zha

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

An alternative to performing the singular value decomposition is to factor a matrix A into matrix presented, where U and V are orthogonal matrices and C is a lower triangular matrix which indicates a separation between two subspaces by the size of its columns. These subspaces are denoted by V = (V1, V2), where the columns of C are partitioned conformally into C = (C1, C2) with ∥ C2 ∥F≤ ε . Here ε is some tolerance. In recent years, this has been called the ULV decomposition (ULVD). If the matrix A results from statistical observations, it is often desired to remove old observations, thus deleting a row from A and its ULVD. In matrix terms, this is called a downdate. A downdating algorithm is proposed that preserves the structure in the downdated matrix C̄ to the extent possible. Strong stability results are proven for these algorithms based upon a new perturbation theory.

Original languageEnglish (US)
Pages (from-to)14-40
Number of pages27
JournalBIT Numerical Mathematics
Volume36
Issue number1
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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