, Volume 43, Issue 3, pp 505517
The Equality Constrained Indefinite Least Squares Problem: Theory and Algorithms
 Adam BojanczykAffiliated withSchool of Electrical and Computer Engineering, Cornell University
 , Nicholas J. HighamAffiliated withSchool of Electrical and Computer Engineering, Cornell University
 , Harikrishna PatelAffiliated withSchool of Electrical and Computer Engineering, Cornell University
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We present theory and algorithms for the equality constrained indefinite least squares problem, which requires minimization of an indefinite quadratic form subject to a linear equality constraint. A generalized hyperbolic QR factorization is introduced and used in the derivation of perturbation bounds and to construct a numerical method. An alternative method is obtained by employing a generalized QR factorization in combination with a Cholesky factorization. Rounding error analysis is given to show that both methods have satisfactory numerical stability properties and numerical experiments are given for illustration. This work builds on recent work on the unconstrained indefinite least squares problem by Chandrasekaran, Gu, and Sayed and by the present authors.
 Title
 The Equality Constrained Indefinite Least Squares Problem: Theory and Algorithms
 Journal

BIT Numerical Mathematics
Volume 43, Issue 3 , pp 505517
 Cover Date
 200309
 DOI
 10.1023/B:BITN.0000007020.58972.07
 Print ISSN
 00063835
 Online ISSN
 15729125
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 equality constrained indefinite least squares problem
 Jorthogonal matrix
 hyperbolic rotation
 hyperbolic QR factorization
 generalized hyperbolic QR factorization
 rounding error analysis
 forward stability
 perturbation theory
 Cholesky factorization
 Industry Sectors
 Authors

 Adam Bojanczyk ^{(1)}
 Nicholas J. Higham ^{(1)}
 Harikrishna Patel ^{(1)}
 Author Affiliations

 1. School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, 148533801, USA