Geodesic
Chebyshev approximation via polynomial mappings and the convergence behaviour of Krylov subspace methods
Electronic transactions on numerical analysis, Tome 12 (2001), pp. 205-215.

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

Summary: Let $\varphi $be a polynomial satisfying some mild conditions. Given a set R $\subset C$, a continuous function m f on R and its best approximation p$\ast $from $\Pi \circ \varphi m$ n - 1 n - 1 with respect to the maximum norm, we show that p$\ast n - 1$ is a best approximation to f $\circ \varphi $on the inverse polynomial image S of R, i.e. $\varphi (S) = R$, where the extremal m m signature is given explicitly. A similar result is presented for constrained Chebyshev polynomial approximation.
Classification : 41A10, 30E10, 65F10
Keywords: Chebyshev polynomial, optimal polynomial, extremal signature, Krylov subspace method, convergence rate 
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     author = {Fischer, Bernd and Peherstorfer, Franz},
     title = {Chebyshev approximation via polynomial mappings and the convergence behaviour of {Krylov} subspace methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {205--215},
     publisher = {mathdoc},
     volume = {12},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2001__12__a2/}
}
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Fischer, Bernd; Peherstorfer, Franz. Chebyshev approximation via polynomial mappings and the convergence behaviour of Krylov subspace methods. Electronic transactions on numerical analysis, Tome 12 (2001), pp. 205-215. http://geodesic.mathdoc.fr/item/ETNA_2001__12__a2/