Backward error and condition number analysis for the indefinite linear least squares problem
Abstract
In this paper, we concentrate on the backward error and condition number of the indefinite least squares problem. For the normwise backward error of the indefinite least square problem, we adopt the linearization method to derive the tight estimations for the exact normwise backward errors. Using the dual techniques of condition number theory \cite{22.0}, we derive the explicit expressions of the mixed and componentwise condition numbers for the linear function of the solution for the indefinite least squares problem. The tight upper bounds for the derived mixed and componentwise condition numbers are obtained, which can be estimated efficiently by means of the classical power method for estimating matrix 1-norm \cite[Chapter 15]{Higham2002Book} during using the QR-Cholesky method \cite{1.0} for solving the indefinite least squares problem. The numerical examples show that the derived condition numbers can give sharp perturbation bound with respect to the interested component of the solution. And the linearization estimations are effective for the normwise backward errors.
Cite
@article{arxiv.1612.06655,
title = {Backward error and condition number analysis for the indefinite linear least squares problem},
author = {Huai-An Diao and Tong-Yu Zhou},
journal= {arXiv preprint arXiv:1612.06655},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1612.03645