Geodesic
Fast multilevel evaluation of smooth radial basis function expansions
Electronic transactions on numerical analysis, Tome 23 (2006), pp. 263-287.

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

Summary: Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data. Notwithstanding, RBFs pose computational challenges, such as the efficient evaluation of an -center $\sterling $RBF expansion at points. A direct summation requires operations. We present a new multilevel method $$########$$§$$###$\ddot \sterling \copyright $###$$ whose cost is only , where is the desired accuracy and is the dimension. The method $$#########$\ddot \sterling $### !###$"#\\%\(') \% 0 applies to smooth radial kernels, e.g., Gaussian, multiquadric, or inverse multiquadric. We present numerical results, discuss generalizations, and compare our method to other fast RBF evaluation methods. This multilevel summation algorithm can be also applied beyond RBFs, to discrete integral transform evaluation, Gaussian filtering and deblurring of images, and particle force summation.$$
Classification : 41A21, 41A30, 41A63, 65D25, 65N06, 65R10, 68Q25
Keywords: radial basis functions, fast multilevel multi-summation, integral transforms, particle interaction 
@article{ETNA_2006__23__a4,
     author = {Livne, Oren E. and Wright, Grady B.},
     title = {Fast multilevel evaluation of smooth radial basis function expansions},
     journal = {Electronic transactions on numerical analysis},
     pages = {263--287},
     publisher = {mathdoc},
     volume = {23},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__23__a4/}
}
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Livne, Oren E.; Wright, Grady B. Fast multilevel evaluation of smooth radial basis function expansions. Electronic transactions on numerical analysis, Tome 23 (2006), pp. 263-287. http://geodesic.mathdoc.fr/item/ETNA_2006__23__a4/