Article

BIT Numerical Mathematics

, Volume 43, Issue 3, pp 505-517

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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Abstract

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.

equality constrained indefinite least squares problem J-orthogonal matrix hyperbolic rotation hyperbolic QR factorization generalized hyperbolic QR factorization rounding error analysis forward stability perturbation theory Cholesky factorization