Asymptotic estimates for the quasi-periodic interpolations. (English) Zbl 1283.42005

Poghosyan, Lusine; Poghosyan, Arnak

Armen. J. Math. 5, No. 1, 34-57 (2013).

Summary: We investigate the convergence of the quasi-periodic interpolation on the entire interval \([-1,1]\) in the \(L_2\)-norm and at the endpoints of the interval by the behavior of the limit function. In both cases we derive exact constants for the main terms of the asymptotic errors. The results of numerical experiments confirm theoretical estimates and show the behavior of the quasi-periodic interpolation for specific functions.

MSC:

42A15	Trigonometric interpolation
65D05	Numerical interpolation

Keywords:

trigonometric interpolation; quasi-periodic interpolation; convergence acceleration; asymptotic estimates