Advertisement

A Survey of Recent Results on Optimal Recovery

  • T. J. Rivlin
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

Abstract

A survey of work in the field of optimal recovery of functions was presented in Micchelli and Rivlin [8] (henceforth referred to as M-R). Our purpose in these three lectures is to reintroduce the notion of optimal recovery and give a selective survey of additional work in that area.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bojanov, B. D., Best quadrature formula for a certain class of analytic functions, Zastos. Mat. 14 (1974), 441–447.zbMATHMathSciNetGoogle Scholar
  2. 2.
    de Boor, C., Computational aspects of optimal recovery, in “Optimal Estimation in Approximation Theory”, (eds. C. A. Micchelli and T. J. Rivlin ), Plenum Press, N. Y., 1977, pp. 69–91.CrossRefGoogle Scholar
  3. 3.
    Boyanov, B. D. (= Bojanov, B.D.), Optimal rate of integration and ɛ-entropy of a class of analytic functions, Mathematical Notes 14 (1973), pp. 551–556. (Trans, from Russian).CrossRefGoogle Scholar
  4. 4.
    Loeb, H. L., A note on optimal integration in H, C. r. Acad. Bulgare Sci. 27 (1974), 615–618.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Loeb, H. L. and H. Werner, Optimal quadrature in Hp spaces, Math. Z. 138 (1974), 111–117.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Melkman, A. A. and C. A. Micchelli, Optimal estimation of linear operators in Hilbert spaces from inaccurate data, IBM Research Report, RC 7175, 1978.Google Scholar
  7. 7.
    Micchelli, C. A., Optimal estimation of smooth functions from inaccurate data, IBM Research Report, RC 7024, 1978.Google Scholar
  8. 8.
    Micchelli, C. A., and T. J. Rivlin, A survey of optimal recovery, in “Optimal Estimation in Approximation Theory”, (eds. C. A. Micchelli and T. J. Rivlin ), Plenum Press, N. Y., 1977, pp. 1–54.CrossRefGoogle Scholar
  9. 9.
    Micchelli, C. A. and T. J. Rivlin, Optimal recovery of best approximations, IBM Research Report, RC 7071, 1978.Google Scholar
  10. 10.
    Newman, D. J., Rational approximation to |x|, Michigan Math. J. 11 (1964), 11–14.Google Scholar
  11. 11.
    Rivlin, T. J., Some aspects of optimal recovery, IBM Research Report, RC 6755, 1977.Google Scholar
  12. 12.
    Stenger, F., Optimal convergence of minimum norm approximations in Hp, Numer. Math. 29 (1978), 345–362.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • T. J. Rivlin
    • 1
  1. 1.Thomas J. Watson Research Center IBMYorktown HeightsUSA

Personalised recommendations