Algebraic properties of discrete box splines
Copyright policy )Algebraic properties of discrete box splines
It is known that the discrete box splines play an important role in the theory of multivariate splines, subdivision algorithms for the computer generation of surfaces, as well as in the theory of partition of numbers. This paper continues the previous works on discrete box splines and subdivision algorithms of \textit{E. Cohen}, \textit{T. Lyche} and \textit{R. Riesenfeld} [Comput. Aided Geom. Des. 1, 131-148 (1984; Zbl 0567.65004)] and of the authors [ibid. 115-129 (1984; Zbl 0581.65011)]. The main purpose of the paper is to discuss linar independence of translates of discrete box splines, which were introduced by these authors as a device for the fast computation of multivariate splines. The results obtained in this paper are applied to the determination of the number of nonnegative integer solutions of a system of linear diophantine equations.
- Bielefeld University Germany
- IBM (United States) United States
multivariate splines, Multidimensional problems, Arithmetic functions; related numbers; inversion formulas, discrete box splines, Combinatorial aspects of matroids and geometric lattices, Spline approximation, subdivision algorithms, Other combinatorial number theory, computer generation of surfaces, linear diophantine equations, fast computation, Difference operators, Diophantine equations in many variables, partition of numbers
multivariate splines, Multidimensional problems, Arithmetic functions; related numbers; inversion formulas, discrete box splines, Combinatorial aspects of matroids and geometric lattices, Spline approximation, subdivision algorithms, Other combinatorial number theory, computer generation of surfaces, linear diophantine equations, fast computation, Difference operators, Diophantine equations in many variables, partition of numbers
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