Hermitian and skew-Hermitian splitting method on a progressive-iterative approximation for least squares fitting

Saknarin Channark; Poom Kumam; Juan Martinez-Moreno; Wachirapong Jirakitpuwapat; Saknarin Channark; Poom Kumam; Juan Martinez-Moreno; Wachirapong Jirakitpuwapat

doi:10.3934/math.2022967

AIMS Mathematics

2022, Volume 7, Issue 9: 17570-17591. doi: 10.3934/math.2022967

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Research article

Hermitian and skew-Hermitian splitting method on a progressive-iterative approximation for least squares fitting

1.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
2.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Faculty of Experimental Science, Department of Mathematics, University of Jaen, Campus Las Lagunillas, s/n, 23071, Jaen, Spain
5.
National Security and Dual-Use Technology Center, National Science and Technology Development Agency (NSTDA), Phathum Thani 12120, Thailand

Received: 18 May 2022 Revised: 17 July 2022 Accepted: 25 July 2022 Published: 29 July 2022
MSC : 41A15, 65D10, 65D17, 65F10, 65F15

To solve the problems of curves and surfaces approximation with normalized totally positive bases, a new progressive and iterative approximation for least square fitting method called HSS-LSPIA is proposed, which is based on the HSS iterative approach for solving linear equations of LSPIA. The HSS-LSPIA format includes two iterations with iterative difference vectors, each of which is distinct from the other. The approximate optimal positive constant, as well as convergence analyses, are provided. Furthermore, the HSS-LSPIA method can be faster than the ELSPIA, LSPIA, and WHPIA methods in terms of convergence speed. Numerical results verify this phenomenon.
- progressive-iterative approximation,
- HSS iteration,
- least square fitting
Citation: Saknarin Channark, Poom Kumam, Juan Martinez-Moreno, Wachirapong Jirakitpuwapat. Hermitian and skew-Hermitian splitting method on a progressive-iterative approximation for least squares fitting[J]. AIMS Mathematics, 2022, 7(9): 17570-17591. doi: 10.3934/math.2022967

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Abstract

To solve the problems of curves and surfaces approximation with normalized totally positive bases, a new progressive and iterative approximation for least square fitting method called HSS-LSPIA is proposed, which is based on the HSS iterative approach for solving linear equations of LSPIA. The HSS-LSPIA format includes two iterations with iterative difference vectors, each of which is distinct from the other. The approximate optimal positive constant, as well as convergence analyses, are provided. Furthermore, the HSS-LSPIA method can be faster than the ELSPIA, LSPIA, and WHPIA methods in terms of convergence speed. Numerical results verify this phenomenon.

References

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