A recurrence relation for chebyshevianB-splines

1. H. Arndt (1978):Konvexe Zerlegung von Differenzenquotienten mit Anwendung auf die Splineinterpolation. In: Numerische Methoden der Approximations Theorie, vol. 4, L. Collatz, G. Meinardus, H. Werner (eds.), ISNM 42 Basel, Birkhauser Verlag: pp. 33–47.

   Google Scholar 

2. W. Boehm (1980):Inserting new knots into B-spline curves. Comput. Aided Design,12: 199–201.

   Google Scholar 

3. C. de Boor (1972):On calculating with B-splines. J. Approx. Theory,6: 50–62.

   Google Scholar 

4. C. Brezinski (1980):The Mühlbach-Neville-Aitken Algorithm and some extensions. BIT,20: 444–451.

   Google Scholar 

5. E. Cohen, T. Lyche, R. Riesenfeld (1980):Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics. Comput. Graphics Image Processing,14: 87–111.

   Google Scholar 

6. W. A. Coppel (1971): Disconjugacy. New York: Springer Verlag. (Lecture Notes in Mathematics, vol. 220).

   Google Scholar 

7. M. Cox (1972):The numerical evaluation of B-splines. J. Inst. Math. Appl.,10: 134–149.

   Google Scholar 

8. J. Favard (1940):Sur l'interpolation. J. Math. Pures Appl.,19: 281–306.

   Google Scholar 

9. S. Karlin (1968): Total Positivity, vol. 1. Stanford, California: Stanford University Press.

   Google Scholar 

10. S. Karlin, W. Studden (1966): Tchebycheff Systems with Applications in Analysis and Statistics. New York: Interscience Publishers.

    Google Scholar 

11. T. Lyche (1983):A Recurrence Relation for Chebyshevian B-Splines. College Station, Texas: Texas A & M University (Report CAT #37, Dept. of Mathematics, Texas A&M Univ., Sept. 1983).

    Google Scholar 

12. T. Lyche, R. Winther (1979):A stable recurrence relation for trigonometric B-splines. J. Approx. Theory,25: 266–279.

    Google Scholar 

13. M. Marsden (1970):An identity for spline functions with applications to variation diminishing spline approximation, J. Approx. Theory,3: 7–49.

    Article  Google Scholar 

14. G. Mühlbach (1973):A recurrence formula for generalized divided differences and some applications. J. Approx. Theory,9: 165–172.

    Google Scholar 

15. G. Mühlbach (1979):A remark on calculating with B-splines. Rev. Roum. Math. Pures Appl.,24: 1449–1450.

    Google Scholar 

16. T. Popoviciu (1958):Sur le reste dans certaines formules linéaires d'approximation de l'analyse. Mathematica (Cluj),1(24)1: 95–142.

    Google Scholar 

17. K. Scherer, L. L. Schumaker (1980):A dual basis for L-splines and applications. J. Approx. Theory,29: 151–169.

    Google Scholar 

18. L. L. Schumaker (1981): Spline Functions: Basic Theory, New York: John Wiley & Sons.

    Google Scholar 

19. L. L. Schumaker (1982):On recursions for generalized splines. J. Approx. Theory,36: 16–31.

    Google Scholar 

20. L. L. Schumaker (1983):On hyperbolic splines. J. Approx. Theory,38: 144–166.

    Google Scholar 

21. D. C. Schweikert (1966):An interpolation curve using a spline in tension. J. Math. Phys.,45: 312–317.

    Google Scholar 

Download references