Linearized estimate of the backward error for the equality constrained indefinite least squares problem

TL;DR

This paper develops a linearization method to accurately estimate the backward error in equality constrained indefinite least squares problems, demonstrating effectiveness through numerical examples.

Contribution

It introduces a new linearization approach to estimate the backward error, providing tight bounds for the normwise backward error in such problems.

Findings

Linearization provides tight estimates for backward errors.

Numerical examples confirm the effectiveness of the method.

The approach improves error estimation accuracy in constrained least squares.

Abstract

In this note, we concentrate on the backward error of the equality constrained indefinite least squares problem. For the normwise backward error of the equality constrained indefinite least square problem, we adopt the linearization method to derive the tight estimate for the exact backward normwise error. The numerical examples show that the linearization estimate is effective for the normwise backward errors.