Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

On monotone and convex spline interpolation


Author: Paolo Costantini
Journal: Math. Comp. 46 (1986), 203-214
MSC: Primary 65D05; Secondary 41A05, 41A15
DOI: https://doi.org/10.1090/S0025-5718-1986-0815841-7
MathSciNet review: 815841
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the problem of existence of monotone and/or convex splines, having degree n and order of continuity k, which interpolate to a set of data at the knots. The interpolating splines are obtained by using Bernstein polynomials of suitable continuous piecewise linear functions; they satisfy the inequality $ k \leqslant n - k$. The theorems presented here are useful in developing algorithms for the construction of shape-preserving splines interpolating arbitrary sets of data points. Earlier results of McAllister, Passow and Roulier can be deduced from those given in this paper.


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

  • [1] P. Costantini, "An algorithm for computing shape-preserving interpolating splines of arbitrary degree," J. Comput. Appl. Math. (Submitted.) MR 948888 (89e:65165)
  • [2] P. Costantini & R. Morandi, "Monotone and convex cubic spline interpolation," Calcolo, v. 21, 1984, pp. 281-294. MR 799625 (86m:65014)
  • [3] P. Costantini & R. Morandi, "An algorithm for computing shape-preserving cubic spline interpolation to data," Calcolo, v. 21, 1984, pp. 295-305. MR 799994 (86j:65016)
  • [4] P. Costantini & R. Morandi, "Piecewise monotone quadratic histosplines." (Preprint.) MR 982231 (90a:65026)
  • [5] C. de Boor & B. Swartz, "Piecewise monotone interpolation," J. Approx. Theory, v. 21, 1977, pp. 411-416. MR 0481727 (58:1826)
  • [6] G. G. Lorentz, Bernstein Polynomials, University of Toronto Press, Toronto, 1953. MR 0057370 (15:217a)
  • [7] D. F. McAllister, E. Passow & J. A. Roulier, "Algorithms for computing shape-preserving spline interpolation to data," Math. Comp., v. 31, 1977, pp. 717-725. MR 0448805 (56:7110)
  • [8] E. Neuman, Shape-Preserving Interpolation by Polynomial Splines, Report no. N112, Institute of Computer Science, Wrocław University, 1982.
  • [9] E. Passow & J. A. Roulier, "Monotone and convex spline interpolation," SIAM J. Numer. Anal., v. 14, 1977, pp. 904-909. MR 0470566 (57:10316)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D05, 41A05, 41A15

Retrieve articles in all journals with MSC: 65D05, 41A05, 41A15


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1986-0815841-7
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society