Unifying unitary and hyperbolic transformations

In this paper, we describe unified formulas for unitary and hyperbolic reflections and rotations, and show how these unified transformations can be used to compute a Hermitian triangular decomposition R ̂ H D R ̂ of a strongly nonsingular indefinite matrix A ̂ given in the form A ̂ =X 1 H X 1+αX 2 H...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2000-09, Vol.316 (1), p.183-197
Main Authors: Bojanczyk, Adam, Qiao, Sanzheng, Steinhardt, Allan O.
Format: Article
Language:English
Subjects:
Cholesky factor modification
Error analysis
Hyperbolic Householder transformation
Hyperbolic rotation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we describe unified formulas for unitary and hyperbolic reflections and rotations, and show how these unified transformations can be used to compute a Hermitian triangular decomposition R ̂ H D R ̂ of a strongly nonsingular indefinite matrix A ̂ given in the form A ̂ =X 1 H X 1+αX 2 H X 2, α=±1 . The unification is achieved by the introduction of signature matrices which determine whether the applicable transformations are unitary, hyperbolic, or their generalizations. We derive formulas for the condition numbers of the unified transformations, propose pivoting strategies for lowering the condition number of the transformations, and present a unified stability analysis for applying the transformations to a matrix.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(00)00108-7