Increases in the quantity of available data have allowed all fields of science to generate more accurate models of multivariate phenomena. Regression and interpolation become challenging when the dimension of data is large, especially while maintaining tractable computational complexity. Regression is a popular approach to solving approximation problems with high dimension; however, there are often advantages to interpolation. This paper presents a novel and insightful error bound for (piecewise) linear interpolation in arbitrary dimension and contrasts the performance of some interpolation techniques with popular regression techniques. Empirical results demonstrate the viability of interpolation for moderately high-dimensional approximation problems, and encourage broader application of interpolants to multivariate approximation in science.

可用数据数量的增加使科学的所有领域都可以生成更准确的多元现象模型。当数据量很大时，尤其是在保持易处理的计算复杂性的同时，回归和内插变得具有挑战性。回归是解决高维逼近问题的一种流行方法。但是，插值通常具有一些优点。本文提出了一种新颖且有见地的误差，适用于任意维（逐段）线性插值，并将某些插值技术的性能与流行的回归技术进行了对比。实验结果证明了插值法对于中等高维逼近问题的可行性，并鼓励将插值法广泛应用于科学中的多元逼近。