Interpolation models are critical for a wide range of applications, from numerical optimization to artificial intelligence. The reliability of the provided interpolated value is of utmost importance, and it is crucial to avoid the insurgence of spurious noise. Noise sources can be prevented using proper countermeasures when the training set is designed, but the data sparsity is inevitable in some cases. A typical example is represented by the application of an optimization algorithm: the area where the minimum or maximum of the objective function is assumed to be present is where new data is abundantly added, but other areas of design variable space are significantly neglected. In these cases, a regularization of the interpolation model becomes absolutely crucial. In this paper we are presenting an approach for the regularization of an interpolator based on the control of its kernel function via the condition number of the self-correlation matrix.

翻译：插值模型在众多应用中至关重要，从数值优化到人工智能领域皆不例外。所提供的插值值可靠性至关重要，避免虚假噪声的出现尤为关键。在设计训练集时，可通过适当对策防止噪声源产生，但在某些情况下数据稀疏性不可避免。典型的例子是优化算法的应用：当目标函数最小值或最大值所在的区域被大量新增数据覆盖时，设计变量空间的其他区域则会被显著忽略。在此类情形下，插值模型的正则化处理变得绝对关键。本文提出了一种基于自相关矩阵条件数控制核函数的插值器正则化方法。