Asymptotic behaviour in linear least squares problems

Date

2010

Authors

Osborne, Michael

Journal Title

Journal ISSN

Volume Title

Publisher

Oxford University Press

Abstract

The asymptotic behaviour of a class of least squares problems when subjected to structured perturbations is considered. It is permitted that the number of rows (observations) in the design matrix can be unbounded while the number of degrees of freedom (variables) is fixed. It is shown that for certain classes of random data the solution sensitivity depends asymptotically on the condition number of the design matrix rather than on its square, which is the generic result for inconsistent systems when the norm of the residual is not small. Extension of these results to the case where the perturbations are due to rounding errors is considered.

Description

Keywords

Keywords: Asymptotic dependence; Condition number; Least squares; Rounding errors; Structured perturbations

Citation

Source

IMA Journal of Numerical Analysis

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

Restricted until

2037-12-31