Geodesic
Fast algorithms for spectral differentiation matrices
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 281-288.

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

Summary: Recently Olver and Townsend presented a fast spectral method that relies on bases of ultraspherical polynomials to give differentiation matrices that are almost banded. The almost-banded structure allowed them to develop efficient algorithms for solving certain discretized systems in linear time. We show that one can also design fast algorithms for standard spectral methods because the underlying matrices, though dense, have the same rank structure as those of Olver and Townsend.
Classification : 65N35, 33C45, 65F05
Keywords: spectral methods, rank-structured matrices 
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     author = {Aurentz, Jared L.},
     title = {Fast algorithms for spectral differentiation matrices},
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     pages = {281--288},
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     volume = {44},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a16/}
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Aurentz, Jared L. Fast algorithms for spectral differentiation matrices. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 281-288. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a16/