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Solving Linear Problems in the Presence of Bounded Data Perturbations

In: Bounding Approaches to System Identification

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  • B. Z. Kacewicz

    (University of Warsaw, Institute of Applied Mathematics)

Abstract

In most computational problems of engineering or numerical analysis available input data (information) is not exact. Perturbations in data may arise for instance from measurement or round-off errors, to mention only these two possible sources. The problem of how inaccuracy in data influences results (for instance, how does it affect a quality of system identification or signal recovery) attracts attention not only for obvious practical reasons, but also motivates a number of theoretical papers. For example, since a long time the case of stochastic errors in information has been studied by statisticians, to mention only the monograph by Wahba,(1) where extensive references to the subject can be found. On the other hand, an active stream of research is based on deterministic assumptions about the noise. Such assumptions are imposed when no appropriate statistical knowledge about the behavior of data errors is available, or simply when statistical analysis is not of interest. The assumption often made in this framework is that errors in information are unknown but bounded. Among many other papers, the bounding approach is discussed in Refs. 2–5.

Suggested Citation

  • B. Z. Kacewicz, 1996. "Solving Linear Problems in the Presence of Bounded Data Perturbations," Springer Books, in: Mario Milanese & John Norton & Hélène Piet-Lahanier & Éric Walter (ed.), Bounding Approaches to System Identification, chapter 3, pages 29-42, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-9545-5_3
    DOI: 10.1007/978-1-4757-9545-5_3
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