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- W2014757722 abstract "We investigate the radial manifolds R n generated by a linear combination of n radial functions on R d . We consider the best approximation of function classes by the manifold R n . In particular, we prove that the deviation of the manifold R n from the Sobolev class W 2 r , d in the Hilbert space L 2 behaves asymptotically as n − r d−1 . We show the connection between the manifold R n and the space of algebraic polynomials P d,s of degree s . Namely, we prove there exist constants c 1 and c 2 such that the space P d,s is either contained or not in R n as n ⩾ c 1 s d −1 or n < c 2 s d −1 , respectively." @default.
- W2014757722 created "2016-06-24" @default.
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- W2014757722 date "2003-01-01" @default.
- W2014757722 modified "2023-10-18" @default.
- W2014757722 title "On best approximation of classes by radial functions" @default.
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- W2014757722 doi "https://doi.org/10.1016/s0021-9045(02)00011-4" @default.
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