A comment on Ewald Quak's ``"About B-splines"


  • Carl de Boor University of Winsconsin-Madison


B-spline, B-spline recurrence, Marsden's identity, knot insertion, Popoviciu, Chakalov


The early contributions to B-spline theory by Tiberiu Popoviciu and by Liubomir Chakalov are recalled.


W. Boehm, Inserting new knots into B-spline curves, CAD, 12, 1980, no. 4, pp.199-201. http://doi.org/10.1016/0010-4485(80)90154-2

C. de Boor and A. Pinkus, The B-spline recurrence relations of Chakalov and of Popoviciu JAT, 124, 2003, no. 1, pp.115-123, http://doi.org/10.1016/S0021-9045(03)00117-5

L. Chakalov, On a certain presentation of the Newton divided differences in interpolation theory and it applications, Annuaire Univ. Sofia, Fiz. Mat. Fakultet, 34, 1938, pp. 353-394 (in Bulgarian).

M.J. Marsden, An identity for spline functions with applications to variation-diminishing spline approximation, JAT, 3, 1970, pp.7-9, http://doi.org/10.1016/0021-9045(70)90058-4

G. Meinardus, Bemerkungen zur Theorie der B-Splines, in Spline-Funktionen, K. Böhmer, G. Meinardus, and W. Schempp Eds., Bibliographisches Institut (Mannheim), 1974, pp.165-175.

T. Popoviciu, Sur quelques propriétés des fonctions d'une ou de deux variables réelles, Mathematica, 8, 1934, pp.1-85.

T. Popoviciu, Sur le prolongement des fonctions convexes d'ordre superieur, Bull. Math. Soc. Roumaine des Sc., 36, 1934, pp.75-108. https://ictp.acad.ro/on-the-prolongation-of-convex-functions-of-higher-order/

E. Quak, About B-splines. Twenty answers to one question: What is the cubic B-spline for the knots -2,-1,0,1,2?, J. Numer. Anal. Approx. Theory, 45, 2016 no. 1, pp. 37-83. https://ictp.acad.ro/jnaat/journal/article/view/1099

I.J. Schoenberg, Spline functions and the problem of graduation, PAMS, 52, 1964, pp. 947-950, http://doi.org/10.1073/pnas.52.4.947




How to Cite

de Boor, C. (2016). A comment on Ewald Quak’s ``"About B-splines". J. Numer. Anal. Approx. Theory, 45(1), 84-86. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1101