Bases for Splines on a Subdivided Domain

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Abstract

Let Sr(Δ) be the module of all splines of smoothness r on the rectilinear partition Δ which subdivides some domain D. Further, let Sr(Γ) be the module of all splines of smoothness r on Γ which also subdivides D, where Γ is a finer subdivision of Δ. We study the relationship between a generating set of Sr(Δ) and a generating set for Sr(Γ). This paper gives an algorithm for extending a generating set for Sr(Δ) to one for for Sr(Γ). This method is built on algebraic properties of splines and the Gröbner Basis Algorithm.

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