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- W1986390133 abstract "For Δ, a triangulated d -dimensional region in R d , let S m r ( Δ ) be the vector space of all C r functions F on Δ such that for any simplex σ ϵ Δ, F¦ σ is a polynomial of degree at most m . S m r ( Δ ) is the often studied vector space of splines on Δ of degree m and smoothness r . We define S r ( Δ ) = ∨ m S m r ( Δ ). S r ( Δ ) is a module over the polynomial ring R [ x 1 ,…, x d ]. In certain cases a module basis for S r ( Δ ) provides vector space bases for the corresponding S m r ( Δ ) via simple linear algebra. In this work we examine that relationship and consider techniques for finding module bases of spaces S r ( Δ ). A basis for S r ( Δ ) is reduced if every element F in S r ( Δ ) can be represented using only basis elements of degree less than the degree of F . We show the relationship between the dimension of the spaces S m r ( Δ ) and the degrees of the reduced basis elements of S r ( Δ ). Ths result leads to techniques for finding module bases. These techniques are used to find module bases for spline spaces on cross-cut grids." @default.
- W1986390133 created "2016-06-24" @default.
- W1986390133 creator A5025209988 @default.
- W1986390133 date "1991-04-01" @default.
- W1986390133 modified "2023-09-25" @default.
- W1986390133 title "Module and vector space bases for spline spaces" @default.
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- W1986390133 doi "https://doi.org/10.1016/0021-9045(91)90113-o" @default.
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