Shape preserving C3 data interpolation and C2 histopolation with splines on threefold refined grids

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 76, Issue 9, 1996, Pages 487-496

  Hess, W ^a   Schmidt, J W ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444455681     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19960760902     Document Type: Article

References (21)

1. 2 interpolants. Numer. Math. 64 (1993), 1-11.
2. BURMEISTER, W.; HESS, W.; SCHMIDT, J. W.: Convex spline interpolants with minimal curvature. Computing 35 (1985), 219-229.
3. COSTANTINI, P.: Algorithms for shape-preserving interpolation. In SCHMIDT, J. W.; SPÄTH, H. (eds.): Splines in numerical analysis. Math. Research 52, Akad. Verlag, Berlin 1989, pp. 31-46.
4. COSTANTINI, P.; MORANDI, R: Monotone and convex cubic spline interpolation. Calcolo 21 (1984), 281-294.
5. GREINER, H.: A survey on univariate data interpolation and approximation by splines of given shape. Math. Comput. Modelling 15 (1991), 97-106.
6. LAHTINEN, A.: Positive Hermite interpolation by quadratic splines. SIAM J. Math. Anal. 24 (1993), 223-233.
7. MORANDI, R.; COSTANTINI, P.: Piecewise monotone quadratic histosplines. SIAM J. Sci. Statist. Comput. 10 (1989), 397-406.
8. MULANSKY, B.; SCHMIDT, J. W.: Powell-Sabin splines in range restricted interpolation of scattered data. Computing 53 (1994), 137-154.
9. 2 interpolation using quartic splines. Numer. Algorithms (to appear).
10. PASSOW, E.; ROULIER, J. A.: Monotone and convex spline interpolation. SIAM J. Numer. Anal. 14 (1977), 904-909.
11. 2 cubic spline interpolation. IMA J. Numer. Anal. 13 (1993), 493-507.
12. SAKAI, M.; USMANI, R. A.: A shape preserving area true approximation of histogram by rational splines. BIT 28 (1988), 329-339.
13. SCHMIDT, J. W.: Staircase algorithm and convex spline interpolation. In BROMMUNDT, E.; GOERISCH, F. (guest eds.): Z. Angew. Math. Mech. 75 (1995), S661-S662.
14. 3. In RÓZSA, P.; SCHMIDT, J. W.; SZABÓ, B. A. (guest eds.): Computers Math. Appl. 31 (1996), 67-79.
15. SCHMIDT, J. W.; HESS, W.: Schwach verkoppelte Ungleichungssysteme und konvexe Spline-Interpolation. Elem. Math. 39 (1984), 85-95.
16. SCHMIDT, J. W.; HESS, W.: Positivity of cubic polynomials on intervals and positive spline interpolation. BIT 28 (1988), 340-352.
17. 2-spline histopolation. J. Approx. Theory 75 (1993), 325-345.
18. 2 interpolation. Numer. Math. 71 (1995), 237-252.
19. SCHMIDT, J. W.; HESS, W.; NORDHEIM, T.: Shape preserving histopolation using rational quadratic splines. Computing 44 (1990), 245-258.
20. SCHUMAKER, L. L.: On shape-preserving quadratic spline interpolation. SIAM J. Numer. Anal. 20 (1983), 854-864.
21. SPÄTH, H.: Eindimensionale Spline-Interpolations-Algorithmen. München-Wien, Oldenbourg-Verlag 1990.