Abstract
We consider the approximation of periodic functions by using the atomic quasiinterpolation of the second and the first order. We obtain expressions for the coefficients of quasiinterpolants and present estimates for errors in the uniform metric.
Similar content being viewed by others
REFERENCES
V. L. Rvachev and V. A. Rvachev, Nonclassical Methods of Approximation Theory in Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1979).
E. A. Fedotova, “On interpolation using atomic functions,” Mat. Met. Analiz. Dinam. Sist., Issue 1, 34–38 (1977).
E. A. Fedotova, Atomic and Spline-Approximation of Solutions of Boundary-Value Problems in Mathematical Physics [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Kharkov (1985).
R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, SIAM, Philadelphia (1971).
N. P. Korneichuk, Splines in Approximation Theory [in Russian], Nauka, Moscow (1984).
Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Kiev (1980).
A. A. Ligun, “On the approximation of differentiable periodic functions by local splines of minimum defect,” Ukr. Mat. Zh., 33, No. 5, 691–693 (1981).
S. G. Dronov and A. A. Ligun, “Some duality relations for local splines,” Ukr. Mat. Zh., 47, No. 1, 12–19 (1995).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Basarab, M.A. Periodic Atomic Quasiinterpolation. Ukrainian Mathematical Journal 53, 1728–1734 (2001). https://doi.org/10.1023/A:1015204229257
Issue Date:
DOI: https://doi.org/10.1023/A:1015204229257