Geodesic
Gegenbauer polynomials and semiseparable matrices
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 26-53
In this paper, we develop a new algorithm for converting coefficients between expansions $\textcent $###$\sterling $########$\ddot $§$\copyright $###

$ in different families of Gegenbauer polynomials up to a finite degree . To this end, we show that the correspond- $

###

$ ing linear mapping is represented by the eigenvector matrix of an explicitly known diagonal plus upper triangular semiseparable matrix. The method is based on a new efficient algorithm for computing the eigendecomposition of such a matrix. Using fast summation techniques, the eigenvectors of an matrix can be computed explicitly with $

###$\ddot $###

$ arithmetic operations and the eigenvector matrix can be applied to an arbitrary vector at cost .$

Classification : 42C10, 42C20, 15A18, 15A23, 15A57, 65T50, 65Y20
Keywords: gegenbauer polynomials, polynomial transforms, semiseparable matrices, eigendecomposition, spectral divide-and-conquer methods 
@article{ETNA_2008__30__a22,
     author = {Keiner,  Jens},
     title = {Gegenbauer polynomials and semiseparable matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {26--53},
     year = {2008},
     volume = {30},
     zbl = {1171.42309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a22/}
}
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%0 Journal Article
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%T Gegenbauer polynomials and semiseparable matrices
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Keiner,  Jens. Gegenbauer polynomials and semiseparable matrices. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 26-53. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a22/