Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Simultaneous spline approximation and interpolation preserving norms


Authors: C. K. Chui, E. R. Rozema, P. W. Smith and J. D. Ward
Journal: Proc. Amer. Math. Soc. 54 (1976), 98-100
DOI: https://doi.org/10.1090/S0002-9939-1976-0387917-8
MathSciNet review: 0387917
Full-text PDF Free Access

Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] C. R. de Boor, On calculating with $ B$-splines, J. Approximation Theory 6 (1972), 50-62. MR 0338617 (49:3381)
  • [2] F. R. Deutsch and P. D. Morris, On simultaneous approximation and interpolation which preserves the norm, J. Approximation Theory 2. (1969), 355-373. MR 40 #6146. MR 0252931 (40:6146)
  • [3] R. Holmes and J. M. Lambert, A geometric approach to property (SAIN), J. Approximation Theory 7 (1973), 132-142. MR 0344769 (49:9508)
  • [4] J. M. Lambert, Simultaneous approximation and interpolation in $ {L_1}$ and $ C(T)$, Pacific J. Math. 45 (1973), 293-296. MR 47 #7295. MR 0318749 (47:7295)
  • [5] -, Simultaneous approximation and interpolation which preserves the norm by cubic splines in $ C[a,b]$ (submitted).
  • [6] W. Wolibner, Sur un polynôme d'interpolation, Colloq. Math. 2 (1951), 136-137. MR 13, 343. MR 0043946 (13:343e)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0387917-8
Keywords: Property SAIN, spline approximation and interpolation, norm preservation, $ B$-spline
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society