Interpolation in a derivative strip

Computing (Vienna/New York)

Volumn 58, Issue 4, 1997, Pages 377-389

  Schmidt, J W ^a,b  

^a Technical University of Dresden ^*

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Placement of additional knots; Quadratic C1 splines; Quartic C2 splines; Refined grids; Strip condition on the derivative

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; INTERPOLATION; SET THEORY; SPLINES;

SPLINE FUNCTIONS;

DATA PROCESSING;

EID: 0031354817     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02684349     Document Type: Article

References (13)

1. Dontchev, A. L.: Best interpolation in a strip. J. Approx. Theory 73, 334-342 (1993).
2. Elfving, T., Andersson, L.-E.: An algorithm for computing constrained smoothing spline functions. Numer. Math. 52, 583-595 (1988).
3. Erdǒs, P., Vértesi, P.: On almost everywhere divergence of Lagrange interpolation polynomials for arbitrary systems of nodes. Acta Math. Acad. Sci. Hung. 36, 71-89 (1980).
4. Herrmann, M., Mulansky, B., Schmidt, J. W.: Scattered data interpolation subject to piecewise quadratic range restrictions. In: Scattered Data Fitting, Cancun 1995 (LeMéhauté, A., Schumaker, L. L, Traversoni, L., eds.). J. Comp. Appl. Math. 73, 209-223 (1996).
5. Heß, W., Schmidt, J. W.: Direct methods for constructing positive spline interpolants. In: Wavelets, Images and Surface Fitting, Chamonix 1993 (Laurent, P. J., Méhauté, A. L., Schumaker, L. L., eds.), pp. 287-294. Wellesley: Peters 1994.
6. Mulansky, B., Schmidt, J. W.: Powell-Sabin splines in range restricted interpolation of scattered data. Computing 53, 137-154 (1994).
7. 2 interpolation using quartic splines, Numer. Alg. 72, 111-124 (1996).
8. 3. In: Numerical Methods, Miskolc 1994 (Rózsa, P., Schmidt, J. W., Szabó, B. A., eds.). Comput. Math. Appl. 31, 67-79 (1996).
9. Schmidt, J. W.: Upper bounds for the second order derivatives in convex spline interpolation. Invest. Oper., to appear.
10. Schmidt. J. W., Heß, W.: Positivity of cubic polynomials on intervals and positive spline interpolation. BIT 28, 340-352 (1988).
11. Schmidt, J. W., Heß, W.: Spline interpolation under two-sided restrictions on the derivatives. Z. Angew. Math. Mech. 69, 353-365 (1989).
12. Schumaker, L. L.: On shape-preserving quadratic spline interpolation. SIAM J. Numer. Anal. 20, 854-864 (1983).
13. 2 histopolation with splines on threefold refined grids. Z. Angew. Math. Mech. 76, 487-496 (1996).