Skip to main content

Towards a unified approach to data smoothing

  • 432 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 909)

Keywords

  • Toeplitz Matrix
  • Smoothing Algorithm
  • Linear Stochastic System
  • Weighted Moving Average
  • Finite Data

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aronsson, G., “Perfect Splines and Nonlinear Optimal Control Theory,” J. of Approx. Th., 25, 142–152 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bauer, F. L., “Beiträge zur Entwicklung numerischer Verfahren für programmgesteuerte Rechenanlagen: II. Direkte Faktorisierung eines Polynoms”, Bayerische Akad. d. Wiss., München (1956).

    MATH  Google Scholar 

  3. Bellman, R., Kashef, B. F., and Vasudevan, R., Splines via Dynamic Programming. JMAA 38, 471–479 (1972).

    MathSciNet  MATH  Google Scholar 

  4. De Figuereido, R. J. P., “LM-g splines”, Technical Report No. 7510. Dept. of EE, Rice University, Houston, Tex. (1975).

    Google Scholar 

  5. Doob, J. L., “Stochastic Processes”, Wiley, (1953). Page 503 is the one referred to in the text.

    Google Scholar 

  6. Duris, C. S., “Discrete Interpolating and Smoothing Spline Functions,” SIAM J. Numer. Anal., 14, 4, (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Greville, T. N. E., “Moving-Weighted-Average Smoothing Extended to the Extremities of the Data”, MRC Tech. Summary Rep. No. 2025, Nov. (1979).

    Google Scholar 

  8. Greville, T. N. E., Trench, W. F., “Band Matrices with Toeplitz Inverses,” Lin. Alg. & its Appl., 27, 199–209 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Jury, E. I., “Theory and Application of the z-transform Method,” J. Wiley, N.Y. (1964).

    Google Scholar 

  10. Kalman, R. E., “New Methods and Results in Linear Prediction and Filtering Theory”, Research Inst. of Adv. Studies, Report No. 61-1, (1961).

    Google Scholar 

  11. Laurent, P. J., “Approximation et Optimisation”, Hermann, (1972).

    Google Scholar 

  12. Lindquist, A., “A Theorem on Duality Between Estimation and Control for Linear Stochastic Systems with Time Delay,” J. Math. Anal. Appl., 37, 516–536 (1972).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Mayne, D. Q., “A Solution of the Smoothing Problem for Linear Dynamic Systems,” Automatica, 4, 73–92 (1966).

    CrossRef  MATH  Google Scholar 

  14. Badawi, F. A., Lindquist, A., Pavon, M., “A Stochastic Realization Approach to the Smoothing Problem,” IEEE Trans. AC, AC-24, 6, 878–888 (Dec. 1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Pontryagin, L. S., “Theorie Mathématique des Processus Optimaux”, Trad, Francaise, Mir., (1974). [Russian Edition, 1959].

    Google Scholar 

  16. Rabiner, L. R., “Theory & Application of Digital Signal Processing”. Prentice-Hall (1975).

    Google Scholar 

  17. Reinsch, C. H., “Smoothing by Spline Functions,” Numer. Math., 10, 177–183 (1967).

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Reinsch, C. H., “Smoothing by Spline Functions II,” Numer. Math., 16, 451–454 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Sidhu, G. S., Desai, U. B., “New Smoothing Algorithms Based on Reversed-Time Lumped Models,” IEEE, Trans. on AC., AC-21, 538–541, (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Trench, W. F., “An Algorithm for the Inversion of Finite Toeplitz Matrices”, J. SIAM, 12, 515–422 (1964).

    MathSciNet  MATH  Google Scholar 

  21. Whittaker, E., Robinson, G., “The Calculus of Observations”, (an Introduction to Numerical Analysis), (1924), 4th. Edition, Dover, (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Farah, J.L. (1982). Towards a unified approach to data smoothing. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092960

Download citation

  • DOI: https://doi.org/10.1007/BFb0092960

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11193-1

  • Online ISBN: 978-3-540-38986-6

  • eBook Packages: Springer Book Archive