有限要素とソボレフ・ノルムを用いたデータ平滑化法

概要

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This paper describes a new data smoothing technique based on a modified least-squares method using finite elements. To smoothly interpolate discrete data, least-squares methods combined with a polynomial or the spline function are commonly used. However, these methods often cause oscillations in the approximation functions and are not so appropriate to calculate derivatives of those function. In order to avoid such oscillations, we propose a new data smoothing technique using finite elements, where the Sobolev norm is minimized. This method takes into account not only the smoothness of the data but also that of the first-order derivative. The present method is applied to one-dimensional as well as two-dimensional problems, and its accuracy and convergency are demonstrated.
社団法人日本機械学会の論文
1988-07-25