ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

Ekaterinburg, Russia 1991 MS Classification: 26, 41, 46, 65 Matveev, Oleg V., Institute of Mathematics and Mechanics, Ekaterinburg, Russia Error estimates for scattered data interpolation Error estimates for interpolation of functions f ∈ W_{p}^{k}(Ω), Ω ⊂ R, on irregular nets Δ ⊂ Ω by D^{m}-splines and radial basis functions are obtained for arbitrary n, m, k, p, Ω, Δ. With the help of D^{m}-splines, bases in Sobolev spaces W_{p}^{k}(Ω) are constructed. Three new constructive interpolation methods are obtained which give the best order of approximation on Sobolev classes of functions f W_{p}^{k}. Reference: O. V. Matveev, Methods of approximate recovering functions given on chaotic nets, Izvestiya RAN. Ser. Mat. 60 (1996), N 5, 111-156 (In Russian; English transl. in Russian Acad. Sci. Izv. Math.)