Konovalov, V. N. Approximation of Sobolev classes by their finite-dimensional sections. (English. Russian original) Zbl 1019.41019 Math. Notes 72, No. 3, 337-349 (2002); translation from Mat. Zametki 72, No. 3, 370-382 (2002). Summary: We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes of periodic functions of a single variable with constraints in \(L_\infty\) or \(L_1\) on higher-order derivatives, we present the exact orders of such widths in the spaces \(L_q\). Cited in 9 Documents MSC: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy Keywords:approximation of Sobolev classes; Sobolev class of periodic functions; width of a function data; Kolmogorov width; relative \(n\)-width of a function class PDF BibTeX XML Cite \textit{V. N. Konovalov}, Math. Notes 72, No. 3, 337--349 (2002; Zbl 1019.41019); translation from Mat. Zametki 72, No. 3, 370--382 (2002) Full Text: DOI