Geodesic
Exact orders of errors in smooth functions approximations
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 45-57

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In this paper exact order estimations of errors in uniform metric approximation of smooth function and its derivatives over several classes are obtained in cases when the function is defined precisely or using its $\delta$-approximation $f_\delta(x)$ in $L_2 [a,b]$ metric. Integral operators with polynomial finite kernels are considered as approximate one. 
@article{ISU_2006_6_1_a5,
     author = {E. V. Shishkova},
     title = {Exact orders of errors in smooth functions approximations},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {45--57},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2006_6_1_a5/}
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E. V. Shishkova. Exact orders of errors in smooth functions approximations. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 45-57. http://geodesic.mathdoc.fr/item/ISU_2006_6_1_a5/