Let W n be the set of 2?-periodic functions with absolutely continuous (n&1)th derivatives and nth derivatives with essential suprema bounded by one. Let n>1. Best uniform approximations to a periodic continuous function from W n are characterized. The result depends upon an analysis of the relatio
โฆ LIBER โฆ
Best linear and nonlinear approximations for smooth functions
โ Scribed by B. E. Klots
- Publisher
- Springer US
- Year
- 1978
- Tongue
- English
- Weight
- 542 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0016-2663
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Error estimates for approximation of functions ~ox,a,0 (x) = ~x,~,l (x) + i~ox,a,2 (X) = [x[)~exp (iA[x[-ยฐ'), A > 0, a :> 0, A e R are given. Let E(f,B, Lp(f~)) denote the error of approximation of f by elements from B in the Lp-metric. Then, it is shown that for polynomial approximation E(~,a,l,Pr,