For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an "uncertainty relation", an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in terms of handling noisy data from challenging computing environments.

翻译：针对散乱数据的径向基函数（RBF）核插值，Schaback于1995年证明了可达逼近误差与底层插值矩阵的条件数无法同时取小。他将这一发现称为“不确定性关系”，其不良后果是RBF核插值易受噪声数据影响。本文提出并研究了一种分布式插值方法，用于管理和量化由插值不可忽略幅值的球面噪声数据所引发的不确定性。我们还展示了数值模拟结果，证明该方法在处理来自具有挑战性的计算环境的噪声数据时具有实用性和鲁棒性。