Progressive Iterative Approximation Method with Memory and Sequences of Weights for Least Square Curve Fitting

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Published: Mar 21, 2023
Keywords:
Least square curve fitting Progressive iterative approximation Sequences of weights

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Saknarin Channark
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, Center of Excellence in Theoretical and Computational Science, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Poom Kumam
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, Center of Excellence in Theoretical and Computational Science, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Parin Chaipunya
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand, Center of Excellence in Theoretical and Computational Science, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Wachirapong Jirakitpuwapat
National Security and Dual-Use Technology Center, National Science and Technology Development Agency, Pathum Thani 12120, Thailand

Abstract

The progressive iterative approximation method with memory and sequences of weights for least square curve fitting (SSLSPIA) is presented in this paper. This method improves the MLSPIA method by varying the weights of the moving average between iterations, using three sequences of weights derived from the singular values of a collocation matrix. It is proved that a sequence of fitting curves with an appropriate alternative of weights converge to the solution of least square fitting and that the convergence rate of the new method is faster than that of the MLSPIA method. Some examples and applications in this paper prove the SSLSPIA method is superior.

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How to Cite
Saknarin Channark, Poom Kumam, Parin Chaipunya, & Wachirapong Jirakitpuwapat. (2023). Progressive Iterative Approximation Method with Memory and Sequences of Weights for Least Square Curve Fitting. Science & Technology Asia, 28(1), 90–107. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248878
Issue
Vol.28 No.1 (January-March 2023)
Section
Physical sciences
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