Relatório de pesquisa 28/08

Optimal Cubature Formulas on Compact Homogeneous Manifolds,  Alexander Kushpel, submitted  Dec. 03.

We find lower bounds for the rate of convergence of optimal cubature formulas on sets of differentiable functions on compact homogeneous manifolds of rank I or two-point homogeneous spaces. It is shown that these lower bounds are sharp in the power scale in the case of $\mathbb{S}^{2}$, the unit sphere in $\mathbb{R}^{3}$.

Mathematics Subject Classifications (2000): 41A46, 42B15

reconstruction, data points, polynomial, volume

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December 04, 2008


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