Оптимальные подпространства для среднеквадратичных приближений классов дифференцируемых функций на отрезке.

Research output: Contribution to journalArticle

Abstract

In this paper, we specify a set of optimal subspaces for L2 approximation of three classes of functions in the Sobolev spaces W (r)2, defined on a segment and subject to certain boundary conditions. A subspace X of dimension not exceeding n is called optimal for a function class A if the best approximation of A by X equals the Kolmogorov n-width of A. These boundary conditions correspond to subspaces of periodically extended functions with symmetry properties. All of the approximating subspaces are generated by equidistant shifts of a single function. The conditions of optimality are given in terms of Fourier coefficients of a generating function. In particular, we indicate optimal spline spaces of all degrees d ≥ r - 1 with equidistant knots of several different types.
Original languageRussian
Pages (from-to)404-417
JournalВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ
Volume7
Issue number3
StatePublished - 2020
Externally publishedYes

Keywords

  • N-widths
  • Spaces of shifts
  • splines
  • поперечники
  • пространства сдвигов
  • сплайны

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