The regularized least-squares radial basis approximation is a kernel-based method to approximate a set of scattered data by a least-squares fit based on an optimization procedure that balances a tradeoff between smoothness of approximation and closeness to the data via a smoothing parameter. This paper suggests the generalized regularized least-squares radial basis approximation for noisy data and its application to the numerical solution of stochastic elliptic PDEs. Numerical observations show that the proposed method is more stable than the typical kernel-based method.

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噪声数据的广义正则化最小二乘逼近及其在随机PDE中的应用

正则化最小二乘径向基近似是基于内核的方法，该方法基于优化过程来通过最小二乘拟合对一组分散的数据进行近似，该优化过程平衡了近似平滑度和通过平滑参数的接近度之间的折衷。本文提出了噪声数据的广义正则化最小二乘径向基近似，并将其应用于随机椭圆PDE的数值解。数值观察表明，该方法比典型的基于核的方法更稳定。