A weighted least squares method for scattered data fitting (Q929907)

The authors present a weighted least squares method in order to find a smooth surface which approximately produces a given set of scattered data points in \(\mathbb{R}^3\). The data are assumed to be contaminated by noise. When the data are reliable, the corresponding weight is 1: when the data are not reliable, the weight (smaller than 1, e.g. \(0.1, 0.01,\dots\)) is chosen according to the size of the noise. Existence and uniqueness of a solution are discussed and an error bound is derived. Some numerical experiments illustrate the performance of the method, which in case of noisy data gives better results than the traditional least squares method.