Improved Least-Squares Progressive Iterative Approximation for Tensor Product Surfaces

Qianqian Hu (), Zhifang Wang and Ruyi Liang
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Qianqian Hu: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
Zhifang Wang: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
Ruyi Liang: School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Mathematics, 2023, vol. 11, issue 3, 1-16

Abstract: Geometric iterative methods, including progressive iterative approximation and geometric interpolation methods, are efficient for fitting a given data set. With the development of big data technology, the number of fitting data points has become massive, and the progressive iterative approximation for least-squares fitting (LSPIA) is generally applied to fit mass data. Combining the Schulz iterative method for calculating the Moore–Penrose generalized inverse matrix with the traditional LSPIA method, this paper presents an accelerated LSPIA method for tensor product surfaces and shows that the corresponding iterative surface sequence converged to the least-squares fitting surface of the given data set. The iterative format is that of a non-stationary iterative method, and the convergence rate increased rapidly as the iteration number increased. Some numerical examples are provided to illustrate that the proposed method has a faster convergence rate.

Keywords: progressive iterative approximation; least-squares fitting; tensor product surface; Schulz iteration; convergence rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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