Data compression with Σ Π -approximations based on splines

Olga E. Baklanova; Vladimir A Vasilenko

Applications of Mathematics (1993)

  • Volume: 38, Issue: 6, page 405-410
  • ISSN: 0862-7940

Abstract

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The paper contains short description of Σ Π -algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.

How to cite

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Baklanova, Olga E., and Vasilenko, Vladimir A. "Data compression with $\Sigma \Pi $-approximations based on splines." Applications of Mathematics 38.6 (1993): 405-410. <http://eudml.org/doc/15761>.

@article{Baklanova1993,
abstract = {The paper contains short description of $\Sigma \Pi $-algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.},
author = {Baklanova, Olga E., Vasilenko, Vladimir A},
journal = {Applications of Mathematics},
keywords = {data compression; $\Sigma \Pi $-approximation; B-splines; colour image processing; continuous and discrete splines; red-green-blue colour images; data compression; -splines-colour imagege processing; sigma-pi algorithm; continuous and discrete splines; red-green-blue colour images; data compression},
language = {eng},
number = {6},
pages = {405-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Data compression with $\Sigma \Pi $-approximations based on splines},
url = {http://eudml.org/doc/15761},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Baklanova, Olga E.
AU - Vasilenko, Vladimir A
TI - Data compression with $\Sigma \Pi $-approximations based on splines
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 6
SP - 405
EP - 410
AB - The paper contains short description of $\Sigma \Pi $-algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.
LA - eng
KW - data compression; $\Sigma \Pi $-approximation; B-splines; colour image processing; continuous and discrete splines; red-green-blue colour images; data compression; -splines-colour imagege processing; sigma-pi algorithm; continuous and discrete splines; red-green-blue colour images; data compression
UR - http://eudml.org/doc/15761
ER -

References

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  1. V. A. Vasilenko, The best finite dimensional Σ Π -approximation, Sov. J. Num. Anal. Math. Mod. 5 (1990), no. 4/5, 435-443. (1990) MR1122378
  2. W. A. Light E. W. Cheney, Approximation theory in tensor product spaces, Lectures Notes in Math., Springer Verlag, 1985. (1985) MR0817984
  3. C. DeBoor, 10.1007/978-1-4612-6333-3, Appl. Math. Sci. 27 (1978). (1978) DOI10.1007/978-1-4612-6333-3

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