Bases for Splines on a Subdivided Domain

Author: Haas R.

Source: Acta Applicandae Mathematicae, Volume 51, Number 2, April 1998 , pp. 113-122(10)

Publisher: Springer

Abstract:

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

Keywords: splines; piecewise polynomials; Gröbner basis

Language: English

Document Type: Regular paper

Affiliations: 1: Smith College, Northampton, MA 01063, U.S.A. e-mail: rhaas@math.smith.edu

Publication date: 1998-04-01

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