On the theorem of curry & schoenberg and the relation between B-spline and box-spline functions

  • Authors:

  • Nicolae Popoviciu;Mioara Boncuţ

  • Affiliations:

  • Hyperion University of Bucharest, Faculty of Mathematics-Informatics, Bucharest, Romania;Lucian Blaga University of Sibiu, Romania

  • Venue:
  • MAMECTIS/NOLASC/CONTROL/WAMUS'11 Proceedings of the 13th WSEAS international conference on mathematical methods, computational techniques and intelligent systems, and 10th WSEAS international conference on non-linear analysis, non-linear systems and chaos, and 7th WSEAS international conference on dynamical systems and control, and 11th WSEAS international conference on Wavelet analysis and multirate systems: recent researches in computational techniques, non-linear systems and control
  • Year:
  • 2011

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Abstract

The work has three sections. Section 1 deals with one theorem of Curry and Schoenberg, defines the B-Spline function and gives the formula of computing the coefficients in B-Spline written as a sum of truncated powers of degree m. Section 2 contains the B-Spline for equidistant knots and an algorithm based on the truncated powers. Section 3 shows a relation between B-Spline and Box-Spline [1].