Geodesic
Data compression with $\Sigma\Pi$-approximations based on splines
Applications of Mathematics, Tome 38 (1993) no. 6, pp. 405-410

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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.
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.
DOI : 10.21136/AM.1993.104563
Classification : 41A15, 65D07, 68U10
Keywords: data compression; $\Sigma\Pi$-approximation; B-splines; colour image processing; continuous and discrete splines; red-green-blue colour images; data compression 
Baklanova, Olga E.; Vasilenko, Vladimir A. Data compression with $\Sigma\Pi$-approximations based on splines. Applications of Mathematics, Tome 38 (1993) no. 6, pp. 405-410. doi: 10.21136/AM.1993.104563
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     title = {Data compression with $\Sigma\Pi$-approximations based on splines},
     journal = {Applications of Mathematics},
     pages = {405--410},
     year = {1993},
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     doi = {10.21136/AM.1993.104563},
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     zbl = {0792.65003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104563/}
}
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[1] V. A. Vasilenko: The best finite dimensional $\Sigma \Pi$-approximation. Sov. J. Num. Anal. Math. Mod. 5 (1990), no. 4/5, 435-443. | MR

[2] W. A. Light E. W. Cheney: Approximation theory in tensor product spaces. Lectures Notes in Math., Springer Verlag, 1985. | MR

[3] C. DeBoor: A practical guide to splines. Appl. Math. Sci. 27 (1978). | DOI

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