Geodesic
Gegenbauer polynomials and semiseparable matrices
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 26-53.

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

Summary: 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},
     publisher = {mathdoc},
     volume = {30},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a22/}
}
TY  - JOUR
AU  - Keiner, Jens
TI  - Gegenbauer polynomials and semiseparable matrices
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 26
EP  - 53
VL  - 30
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__30__a22/
LA  - en
ID  - ETNA_2008__30__a22
ER  - 
%0 Journal Article
%A Keiner, Jens
%T Gegenbauer polynomials and semiseparable matrices
%J Electronic transactions on numerical analysis
%D 2008
%P 26-53
%V 30
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2008__30__a22/
%G en
%F ETNA_2008__30__a22
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/