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On the Orders of Nonlinear Approximations for Classes of Functions of Given Form.
- Source :
- Mathematical Notes; Jul/Aug2005, Vol. 78 Issue 1/2, p88-104, 17p
- Publication Year :
- 2005
-
Abstract
- Suppose that Δ is the set of functions x: I → ℝ on a finite interval I such that the divided differences [ x; t<subscript>0</subscript>,..., t<subscript> s</subscript>] of order <subscript>s</subscript> ∈ ℕ of these functions are nonnegative for all collections from ( s +1) different points t<subscript>0</subscript>,..., t<subscript> s</subscript> ∈ I. For all s ∈ ℕ and 1 ≤ p ≤ ∞, we establish exact orders of best approximations by splines with free nodes and rational functions in the metrics of L<subscript> p</subscript> for classes $$\Delta _ + ^s B_p : = \Delta _ + ^s \cap B_p$$ , where B<subscript> p</subscript> is the unit ball in L<subscript> p</subscript>. We also establish the asymptotics of pseudodimensional widths in L<subscript> p</subscript> of these classes of functions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 78
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 17941305
- Full Text :
- https://doi.org/10.1007/s11006-005-0102-3