Algebraic properties and perturbation results for the indefinite least squares problem with equality constraints

Abstract

In this paper, several equivalent systems without constraints of the indefinite least squares problem with equality constraints (ILSE) are established. We also derive the perturbation results for the ILSE problem and illustrate our results with numerical tests.

Keywords:

• equality constrained indefinite least squares problem
• KKT system
• the method of weighting
• generalized hyperbolic QR factorization
• perturbation theory

2000 AMS Subject Classification :

• 65F20
• 65G05

Acknowledgements

The work of Qiaohua Liu was supported by Shanghai Municipal R&D Special-purpose Grant for Selectively Culturing Excellent Young Teachers in Universities and Colleges (B. 99-0303-06-040) and Shanghai Municipal Education Commission (06AZ088). The work of Minghui Wang was supported by NSFC under grant no. 10771073.