扩展欧几里得空间和球面上径向逼近的误差估计范围
Extending the range of error estimates for radial approximation in Euclidean space and on spheres
AI总结：
通过适配Schaback的误差加倍技巧，为光滑性介于通常原生空间和双倍光滑性子空间之间的函数提供径向插值的误差估计，并证明插值误差的伪导数收敛性。
摘要：
我们将Schaback的误差加倍技巧[R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.]进行适配，以给出光滑性（在某种意义上）介于通常原生空间和双倍光滑性子空间之间的函数的径向插值误差估计。我们针对R^d的有界子集和球面都进行了处理。在实现最终目标的过程中，我们还展示了插值误差的伪导数的收敛性。
英文摘要：
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
