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
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 
@article{ETNA_2001__12__a2,
     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},
     year = {2001},
     volume = {12},
     zbl = {0978.41004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2001__12__a2/}
}
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%A Peherstorfer,  Franz
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%D 2001
%P 205-215
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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/