Geodesic
Computation with wavelets in higher dimensions
Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 523-532.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In dimension $d$, a lattice grid of size $N$ has $N^d$ points. The representation of a function by, for instance, splines or the so-called non-standard wavelets with error $\varepsilon$ would require $O(\varepsilon^{-ad})$ lattice point values (resp. wavelet coefficients), for some positive $a$ depending on the spline order (resp. the properties of the wavelet). Unless $d$ is very small, we easily will get a data set that is larger than a computer in practice can handle, even for very moderate choices of $N$ or $\varepsilon$. I discuss how to organize the wavelets so that functions can be represented with $$O((\log(1/\varepsilon))^{a(d- 1)}\varepsilon^{- a})$$ coefficients. Using wavelet packets, the number of coefficients may be further reduced.
Classification : 42C40, 65D07
Keywords: higher dimensions, wavelets, lattice point values, wavelet coefficients 
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     author = {Str\"omberg, Jan-Olov},
     title = {Computation with wavelets in higher dimensions},
     journal = {Documenta mathematica},
     pages = {523--532},
     publisher = {mathdoc},
     volume = {ICM Berlin 1998, Vol. III},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1998__S9__a27/}
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Strömberg, Jan-Olov. Computation with wavelets in higher dimensions. Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 523-532. http://geodesic.mathdoc.fr/item/DOCMA_1998__S9__a27/