The equality constrained indefinite least squares problem: Theory and algorithms

Adam Bojanczyk, Nicholas J. Higham, Harikrishna Patel

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)505-517
    Number of pages12
    JournalBIT Numerical Mathematics
    Issue number3
    Publication statusPublished - Sept 2003


    • Cholesky factorization
    • Equality constrained indefinite least squares problem
    • Forward stability
    • Generalized hyperbolic QR factorization
    • Hyperbolic QR factorization
    • Hyperbolic rotation
    • J-orthogonal matrix
    • Perturbation theory
    • Rounding error analysis


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