论文标题
四分之一的$ l^p $ - 立方riemannian花键
Quartic $L^p$-convergence of cubic Riemannian splines
论文作者
论文摘要
我们证明，随着插值网格的网格大小趋向于零，曲线的立方样条插值将曲线的四分之一收敛。与在欧几里得空间中的立方样条插值相比，该结果是经典的，插值算子不再是线性的。尽管如此，线性设置的概念仍可以推广到Riemannian案例，我们尝试使用内在的Riemannian配方，并尽可能避免使用图表。
We prove quartic convergence of cubic spline interpolation for curves into Riemannian manifolds as the grid size of the interpolation grid tends to zero. In contrast to cubic spline interpolation in Euclidean space, where this result is classical, the interpolation operator is no longer linear. Still, concepts from the linear setting may be generalized to the Riemannian case, where we try to use intrinsic Riemannian formulations and avoid charts as much as possible.
