Optimal recovery of isotropic classes of rth differentiable multivariate functions
- 131 Downloads
Estimates are given for the optimal recovery of functions in d variables, which are known to have (r−1)st absolutely continuous and rth bounded derivatives in any direction over, either a bounded convex d-dimensional body G, or which are periodic over a d dimensional lattice. The information is the values of the function and all its derivatives of order less than r at n points. We obtain some asymptotic estimates for this problem, and some exact results for several special cases which contain the results of Babenko, Borodachov, and Skorokhodov.
KeywordsOptimal recovery Approximation of function Differentiable function Sphere covering problem
Mathematics Subject Classification (2010)41A25 41A44 41A63
- 2.Babenko, V.: On optimal piecewise linear interpolation of continuous mappings. In: Investigations in Current Problems in Summation and Approximation of Functions and Their Applications 3–7. (1980). Gos. Univ. Dnepropetrovsk (in Russian) Google Scholar
- 11.Sun, Y.: Approximation Theory of Functions, vol. I. Beijing Normal University Press, Beijing (1990) (In Chinese) Google Scholar