Scattered Data Approximation of Noisy Data via Iterated Moving Least Squares
نویسندگان
چکیده
In this paper we focus on two methods for multivariate approximation problems with non-uniformly distributed noisy data. The new approach proposed here is an iterated approximate moving least-squares method. We compare our method to ridge regression which filters out noise by using a smoothing parameter. Our goal is to find an optimal number of iterations for the iterative method and an optimal smoothing parameter for ridge regression so that the corresponding approximants do not exactly interpolate the given data but are reasonably close. For both approaches we implement variants of leave-one-out cross-validation in order to find these optimal values. The shape parameter for the basis functions is also optimized in our algorithms. §
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