On one approach to local surface smoothing

Nikolay Dikoussar; Csaba Török

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 533-546
  • ISSN: 0023-5954

Abstract

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A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.

How to cite

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Dikoussar, Nikolay, and Török, Csaba. "On one approach to local surface smoothing." Kybernetika 43.4 (2007): 533-546. <http://eudml.org/doc/33878>.

@article{Dikoussar2007,
abstract = {A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.},
author = {Dikoussar, Nikolay, Török, Csaba},
journal = {Kybernetika},
keywords = {data smoothing; least squares and related methods; linear regression; approximation by polynomials; interpolation; computer aided design (modeling of curves and surfaces); surface approximation; numerical examples; data smoothing; least squares; linear regression; approximation by polynomials; Interpolation; computer aided design; surface approximation; normal equations; stability; algorithms},
language = {eng},
number = {4},
pages = {533-546},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On one approach to local surface smoothing},
url = {http://eudml.org/doc/33878},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Dikoussar, Nikolay
AU - Török, Csaba
TI - On one approach to local surface smoothing
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 533
EP - 546
AB - A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
LA - eng
KW - data smoothing; least squares and related methods; linear regression; approximation by polynomials; interpolation; computer aided design (modeling of curves and surfaces); surface approximation; numerical examples; data smoothing; least squares; linear regression; approximation by polynomials; Interpolation; computer aided design; surface approximation; normal equations; stability; algorithms
UR - http://eudml.org/doc/33878
ER -

References

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  10. Loader C., Smoothing: Local regression techniques In: Handbook of Computational Statistics (J, E. Gentle et al., eds.), Springer–Verlag, Berlin 2004 MR2090154
  11. Mallat S., A Wavelet Tour of Signal Processing, Academic Press, New York 1999 Zbl1170.94003MR2479996
  12. Riplay B. D., Pattern Recognition and Neural Networks, Cambridge University Press, Cambridge 1996 MR1438788
  13. Seber G. A., Linear Regression Analysis, Wiley, New York 1977 Zbl1029.62059MR0436482
  14. Török, Cs., 4-point transforms and approximation, Comput. Phys. Comm. 125 (2000), 154–166 
  15. Török, Cs., Dikoussar N. D., Approximation with discrete projective transformation, Comput. Math. Appl. 38 (1999), 211–220 (1999) Zbl1058.65506MR1718884
  16. Török, Cs., Kepič T., Data compression based on auto-tracking piecewise cubic approximation and wavelets, In: SICAM Plovdiv 2005, p. 274 
  17. Wahba G., Spline Models for Observational Data, SIAM, Philadelphia 1990 Zbl0813.62001MR1045442

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