The Computational Cost of Simplex Spline Functions.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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All computational schemes for simplex spline functions to date rely both on the recurrence relation for these functions and the standard construction of the simplex spline basis. Under these conditions, for numerical methods for computing simplex spline functions to be a useful as possible, it is necessary to find ways of implementing the recurrence relation as efficiently as possible. This paper shows that as efficiently as possible is still not very efficient. This implies that truly fast algorithms which have not yet been developed will have to either abandon the recurrence relation or the standard construction of the simplex spline basis. Keywords B splines Multivariate analysis.
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