A structurally backward stable algorithm for solving the indefinite least squares problem with equality constraints

Mastronardi, Nicola;Van Dooren, Paul
(2015) IMA Journal of Numerical Analysis — Vol. 35, n° 1, p. 107-132 (2015)

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Authors
  • Mastronardi, NicolaIstituto per le Applicazioni del Calcolo M. Picone, Consiglio Nationale delle Ricerche, Bari, Italy
    Author
  • Van Dooren, PaulUCLouvain
    Collaborator
Abstract
The equality constrained indefinite least squares problem involves the minimization of an indefinite quadratic form subject to a linear equality constraint. In this paper, we study this problem and present a numerical method that is proved to be backward stable in a strict sense, i.e., that the computed solution satisfies a slightly perturbed equality constrained indefinite least squares problem. We also perform a sensitivity analysis of this problem and derive bounds for the accuracy of the computed solution. We give several numerical experiments to illustrate these results.
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Mastronardi, N. (2015). A structurally backward stable algorithm for solving the indefinite least squares problem with equality constraints. IMA Journal of Numerical Analysis, 35(1), 107-132. https://doi.org/10.1093/imanum/dru004 (Original work published 2015)