Solving Linear Problems in the Presence of Bounded Data Perturbations

  • B. Z. Kacewicz

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.

Keywords

Linear Problem Minimal Error Minimal Diameter Signal Recovery Linear Normed Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Wahba, SIAM (1990).Google Scholar
  2. 2.
    M. Milanese and A. Vicino, in: Bounding Approaches to System Identification (Milanese et al., eds.) Plenum Press, New York, Chap. 2 (1996).Google Scholar
  3. 3.
    S. M. Markov and E. D. Popowa, in: Bounding Approaches to System Identification (Milanese et al., eds.) Plenum Press, New York, Chap. 9 (1996).Google Scholar
  4. 4.
    G. Belforte and T. T. Tay, in: Bounding Approaches to System Identification (Milanese et al., eds.) Plenum Press, New York, Chap. 6 (1996).Google Scholar
  5. 5.
    G. Favier and L. V. Arruda, in: Bounding Approaches to System Identification (Milanese et al., eds.) Plenum Press, New York, Chap. 4 (1996).Google Scholar
  6. 6.
    A. J. Helmicki, C.A. Jacobson, and C.N. Nett, IEEE Trans. Autom. Control 36, 1163 (1991).MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    B. Z. Kacewicz and L. Plaskota, Math. Comp. 59, 503 (1992).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    B. Z. Kacewicz and L. Plaskota, Numer Funct. Anal Optim. 11, 511–529 (1990).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    B. Z. Kacowicz and M. Kowalski, Int. J. Adapt. Control Signal Proc., in press.Google Scholar
  10. 10.
    J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski, Information Based Complexity, Academic Press, New York (1988).MATHGoogle Scholar
  11. 11.
    C. A. Micchelli and T. J. Rivlin, in: Optimal Estimation in Approximation Theory (C. A. Micchelli and T. J. Rivlin, eds.) Plenum Press, New York (1977).Google Scholar
  12. 12.
    A. G. Marchuk and K.Y. Osipenko, Math. Notes 17, 207 (1975).MATHCrossRefGoogle Scholar
  13. 13.
    A. Melkman and C. A. Micchelli, SIAM J. Numer. Anal. 16, 87 (1979).MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    D. Lee, T. Pavlidis, and G. W. Wasilkowski, J. Complexity 3, 359 (1987).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • B. Z. Kacewicz
    • 1
  1. 1.Institute of Applied MathematicsUniversity of WarsawWarsawPoland

Personalised recommendations