## 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 = (V_{1}, V_{2}), where the columns of C are partitioned conformally into C = (C_{1}, C_{2}) with ∥ C_{2} ∥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 language | English (US) |
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Pages (from-to) | 14-40 |

Number of pages | 27 |

Journal | BIT Numerical Mathematics |

Volume | 36 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

## All Science Journal Classification (ASJC) codes

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