Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Splines with nonnegative $ B$-spline coefficients


Authors: C. de Boor and James W. Daniel
Journal: Math. Comp. 28 (1974), 565-568
MSC: Primary 65D15
MathSciNet review: 0378357
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the question of the approximation of nonnegative functions by nonnegative splines of order k (degree $ < k$) compared with approximation by that subclass of nonnegative splines of order k consisting of all those whose B-spline coefficients are nonnegative; while approximation by the former gives errors of order $ {h^k}$, the latter may yield only $ {h^2}$. These results are related to certain facts about quasi-interpolants.


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

  • [1] C. de Boor, "On uniform approximation by splines," J. Approximation Theory, v. 1, 1968, pp. 219-235. MR 39 #1866. MR 0240519 (39:1866)
  • [2] C. de Boor & G. J. Fix, "Spline approximation by quasi-interpolants," J. Approximation Theory, v. 8, 1973, pp. 19-45. MR 0340893 (49:5643)
  • [3] H. Burchard, "Extremal positive splines with applications to interpolation and approximation by geheralized convex functions," Symposium on Approximation Theory, University of Texas, Austin, Texas, 1973. MR 0338620 (49:3384)
  • [4] H. B. Curry & I. J. Schoenberg, "On Polya frequency functions. IV: The fundamental spline functions and their limits," J. Analyse Math., v. 17, 1966, pp. 71-107. MR 36 #1884. MR 0218800 (36:1884)
  • [5] M. J. Marsden, "An identity for spline functions with applications to variation-diminishing spline approximation," J. Approximation Theory, v. 3, 1970, pp. 7-49. MR 40 #7682. MR 0254474 (40:7682)
  • [6] I. J. Schoenberg, "On spline functions," in Inequalities, (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 255-291. MR 36 #6848. MR 0223801 (36:6848)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D15

Retrieve articles in all journals with MSC: 65D15


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0378357-2
PII: S 0025-5718(1974)0378357-2
Keywords: Nonnegative splines, one-sided approximation, splines, approximation
Article copyright: © Copyright 1974 American Mathematical Society