Direct and converse results by rational operators

Constructive Approximation

Volumn 12, Issue 2, 1996, Pages 271-285

  Della Vecchia, B ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Direct and converse results; Ditzian Totik moduli of smoothness; Rational approximation; Shepard operators

Indexed keywords

EID: 0030542675     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003659900013     Document Type: Article

References (18)

1. R. E. BARNHILL, R. P. DUBE, F. F. LITTLE (1983): Properties of Shepard's surfaces. Rocky Mountain J. Math., 13:365-382.
2. H. BERENS, G. G. LORENTZ (1972): Inverse theorems for Bernstein polynomials. Indiana Univ. Math. J., 21:693-708.
3. L. P. BOS, K. SALKAUSKAS (1989): Moving least-squares are Backus-Gilbert optimal. J. Approx. Theory, 59:267-275.
4. G. CRISCUOLO, G. MASTROIANNI (1993): Estimates of the Shepard interpolators procedure. Acta Math. Hungar., 61:79-91.
5. B. DELLA VECCHIA, G. MASTROIANNI (1991): Pointwise simultaneous approximation by rational operators. J. Approx. Theory, 65:140-150.
6. B. DELLA VECCHIA, G. MASTROIANNI (1991): Pointwise estimates of rational operators based on general distributions of knots. Facta Univ. Nis, Ser. Math. Inform., 6:63-72.
7. 1 norm. J. Comput. Appl. Math., 53:333-339.
8. B. DELLA VECCHIA, G. MASTROIANNI (1995): On functions approximation by Shepard-type operators -a survey. In: Approximation Theory, Wavelets and Applications (S. P. Singh, ed.). Dordrecht: Kluwer, pp. 335-346.
9. B. DELLA VECCHIA, G. MASTROIANNI, V. TOTIK (1990): Saturation of the Shepard operators. J. Approx. Theory and Its Appl., 6(4):76-84.
10. Z. DITZIAN, V. TOTIK (1987): Moduli of Smoothness. New York: Springer-Verlag.
11. R. FARWIG (1986): Rate of convergence of Shepard's global interpolation formula. Math. Comp., 46:577-590.
12. T. FOLEY (1986): Scattered data interpolation and approximation with error bounds. Comput. Aided Geom. Design, 3:163-177.
13. G. MASTROIANNI, P. VERTESI (1993): Approximation by some operators using certain new moduli of continuity. Rend. Circ. Mat. Palermo, 33:387-397.
14. D. J. NEWMANN, T. J. RIVLIN (1982): Optimal Universally Stable Interpolation. Research Report, IBM Research Division.
15. D. SHEPARD (1968): A two-dimensional interpolation function for irregularly spaced points. Proc. 1968 ACM National Conference, pp. 517-524.
16. G. SOMORJAI (1978): On a saturation problem. Acta Math. Acad. Sci. Hungar., 32:377-381.
17. J. SZABADOS (1976): On a problem of R. DeVore. Acta Math. Acad. Sci. Hungar., 27:219-223.
18. J. SZABADOS, Direct and converse approximation theorems for the Shepard operator. J. Approx. Theory and Its Appl., 7(3):63-76.