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Starting with a partition of a rectangular box into subboxes, it is shown how to construct a natural tetrahedral (type-4) partition and associated trivariate C 1 quintic polynomial spline spaces with a variety of useful properties, including stable local bases and full approximation power. It is also shown how the spaces can be used to solve certain Hermite and Lagrange interpolation problems. 相似文献
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We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. 相似文献
4.
Trivariate Cr macroelements defined in terms of polynomials of degree 8r + 1 on tetrahedra are analyzed. For r = 1,2, these spaces reduce
to well-known macroelement spaces used in data fitting and in the finite-element method.
We determine the dimension of these spaces, and describe stable local minimal determining sets and nodal minimal determining
sets. We also show that the spaces approximate smooth functions to optimal order. 相似文献
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The problem of computing the dimension of spaces of splines whose elements are piecewise polynomials of degreed withr continuous derivatives globally has attracted a great deal of attention recently. We contribute to this theory by obtaining dimension formulae for certain spaces of super splines, including the case where varying amounts of additional smoothness is enforced at each vertex. We also explicitly construct minimally supported bases for the spaces. The main tool is the Bernstein-Bézier method.Communicated by Klaus Höllig. 相似文献
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Linear conditions for a C 0 spline to be convex are developed and used to create some convexity preserving interpolation and approximation methods. 相似文献
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Peter Alfeld Larry L. Schumaker Tatyana Sorokina 《Advances in Computational Mathematics》2010,32(4):381-391
A variant of the classical C
1 Powell-Sabin-12 macro-element is defined that has the same approximation power, but has fewer degrees of freedom and only
requires vertex data. The same idea is then applied to a related C
1 trivariate macro-element. 相似文献