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On extended progressive and iterative approximation for least squares fitting

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Abstract

The progressive and iterative approximation method for least square fitting (LSPIA) (Deng and Lin in Comput Aided Des 47:32–44, 2014) is an efficient method for fitting a large number of data points. By introducing the global and local relaxation parameters, we develop an extended LSPIA (ELSPIA) method which includes the LSPIA method as its special case. The ELSPIA method constructs the sequence of curves and surfaces by adjusting the control points with the outer and inner iteration. It is proved that the sequence of curves and surfaces converges to the least square fitting curve and surface, respectively, even when the collocation matrix is not of full column rank. The ELSPIA method is flexible to allow the local adjustment of the control points. Moreover, the convergence rate of the ELSPIA method can be faster than that of the LSPIA method under the same assumption. Numerical results verify this phenomenon.

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  1. China Jiliang University, Hangzhou, China

    Huidi Wang

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  1. Huidi Wang
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Correspondence to Huidi Wang.

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This work was supported by the National Natural Science Foundation of China under Grant No. 11871430. The author declares that she has no conflict of interest.

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Wang, H. On extended progressive and iterative approximation for least squares fitting. Vis Comput 38, 591–602 (2022). https://doi.org/10.1007/s00371-020-02036-8

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