Simultaneous spline approximation and interpolation preserving norms
HTML articles powered by AMS MathViewer
- by C. K. Chui, E. R. Rozema, P. W. Smith and J. D. Ward
- Proc. Amer. Math. Soc. 54 (1976), 98-100
- DOI: https://doi.org/10.1090/S0002-9939-1976-0387917-8
- PDF | Request permission
Abstract:
In this paper, it is proved that splines of order $k(k \geqslant 2)$ have property SAIN. The proof of this result is based on the important properties of $B$-splines.References
- Carl de Boor, On calculating with $B$-splines, J. Approximation Theory 6 (1972), 50–62. MR 338617, DOI 10.1016/0021-9045(72)90080-9
- Frank Deutsch and Peter D. Morris, On simultaneous approximation and interpolation which preserves the norm, J. Approximation Theory 2 (1969), 355–373. MR 252931, DOI 10.1016/0021-9045(69)90004-5
- Richard Holmes and Joseph Lambert, A geometrical approach to property (SAIN), J. Approximation Theory 7 (1973), 132–142. MR 344769, DOI 10.1016/0021-9045(73)90060-9
- Joseph M. Lambert, Simultaneous approximation and interpolation in $L_{1}$ and $C(T)$, Pacific J. Math. 45 (1973), 293–296. MR 318749 —, Simultaneous approximation and interpolation which preserves the norm by cubic splines in $C[a,b]$ (submitted).
- W. Wolibner, Sur un polynôme d’interpolation, Colloq. Math. 2 (1951), 136–137 (French). MR 43946, DOI 10.4064/cm-2-2-136-137
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 98-100
- DOI: https://doi.org/10.1090/S0002-9939-1976-0387917-8
- MathSciNet review: 0387917