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


  • Carl de Boor University of Winsconsin-Madison, USA




B-spline, B-spline recurrence, Marsden's identity, knot insertion, Popoviciu, Chakalov
Abstract views: 947


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


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[B80] W. Boehm, Inserting new knots into B-spline curves, Computer-Aided Design, 12 (1980) no. 4, pp.199-201, http://dx.doi.org/10.1016/0010-4485(80)90154-2 DOI: https://doi.org/10.1016/0010-4485(80)90154-2

[BP03] C. de Boor and A. Pinkus, The B-spline recurrence relations of Chakalov and of Popoviciu, J. Approx. Theory, 124 (2003) no. 1, pp.115-123, http://dx.doi.org/10.1016/S0021-9045(03)00117-5 DOI: https://doi.org/10.1016/S0021-9045(03)00117-5

[C38] 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).

[Ma70] M.J. Marsden, An identity for spline functions with applications to variation-diminishing spline approximation, J. Approx. Theory, 3 (1970), pp.7-49, http://dx.doi.org/10.1016/0021-9045(70)90058-4 DOI: https://doi.org/10.1016/0021-9045(70)90058-4

[Me74] G. Meinardus, Bemerkungen zur Theorie der B-Splines, in Spline-Funktionen (K. Bohmer, G. Meinardus, and W. Schempp Eds.), Bibliographisches Institut (Mannheim), 1974, pp.165-175.

[P34a] T. Popoviciu, Sur quelques proprietes des fonctions d’une ou de deux variables reel les, Mathematica, 8 (1934), pp.1-85. Retrieved on October 3rd, 2016, from http://ictp.acad.ro/popoviciu

[P34b] T. Popoviciu, Sur le prolongement des fonctions convexes d’ordre superieur, Bull. Math. Soc. Roumaine des Sc.,36 (1934), pp.75-108. Retrieved on October 3rd, 2016, from http://ictp.acad.ro/popoviciu

[Q] 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, http://ictp.acad.ro/jnaat/journal/issue/view/2016-vol45-no1 DOI: https://doi.org/10.33993/jnaat451-1099

[S64] I.J. Schoenberg, Spline functions and the problem of graduation, Proc. Amer. Math. Soc., 52 (1964), pp.947-950, http://dx.doi.org/10.1073/pnas.52.4.947 DOI: https://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. https://doi.org/10.33993/jnaat451-1101