A NEW PARAMETERIZED MATRIX SPLITTING PRECONDITIONER FOR THE SADDLE POINT PROBLEMS

Li-Tao Zhang; Guang-Xu Zhu

doi:10.11948/20240515

2025 Volume 15 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(5): 2747-2760

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Li-Tao Zhang, Guang-Xu Zhu. A NEW PARAMETERIZED MATRIX SPLITTING PRECONDITIONER FOR THE SADDLE POINT PROBLEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2747-2760. doi: 10.11948/20240515

Citation:

Li-Tao Zhang, Guang-Xu Zhu. A NEW PARAMETERIZED MATRIX SPLITTING PRECONDITIONER FOR THE SADDLE POINT PROBLEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2747-2760. doi: 10.11948/20240515

A NEW PARAMETERIZED MATRIX SPLITTING PRECONDITIONER FOR THE SADDLE POINT PROBLEMS

Li-Tao Zhang^1, ,,
Guang-Xu Zhu^2,

1.
School of Mathematics, Zhengzhou University of Aeronautics, Street, 450046, China
2.
School of Aerospace Engineering, Zhengzhou University of Aeronautics, 450046, China

Author Bio: Email: 18749538109@163.com (G.-X. Zhu)
Corresponding author: Email: litaozhang@163.com(L.-T. Zhang)
Fund Project: This research of this author is supported by the National Natural Science Foundation of China (11226337, 11501525, 12401655), Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions (25ZX013), Scientific Research Team Plan of Zhengzhou University of Aeronautics (23ZHTD01003), Key Scientific Research Projects Plan in Henan Higher Education Institutions (24A170031), Henan science and technology research program (212102110206, 222102110404, 202102310942), Henan College Students' innovation training program (s202110485045) and college students' innovation training program (2021-70), Key projects of colleges and universities in Henan Province (22A880022), Henan Province General Project (242300421373), Scientific and Technological Project in Henan Province (242102210114), Henan Province Higher Education Teaching Reform Research and Practice Project (2024SJGLX0150, 2024SJGLX0410)

Abstract

Abstract

Recently, Zheng and Lu [International Journal of Computer Mathematics, 96(1): 1-17, DOI: 10.1080/00207160.2017.1420179] constructed a parameterized matrix splitting (PMS) preconditioner for the large sparse saddle point problems, and gave the corresponding theoretical analysis and numerical experiments. In this paper, based on the parameterized matrix splitting, we generalize the PMS algorithms and further present the new parameterized matrix splitting (NPMS) preconditioner for the saddle point problems. Moreover, by similar theoretical analysis, we analyze the convergence conditions of the corresponding matrix splitting iteration methods and preconditioning properties of the NPMS preconditioned saddle point matrices. Finally, one example is provided to confirm the effectiveness.
- Matrix splittings /
- saddle point problem /
- convergence /
- preconditioner /
- eigenvalue
MSC: 65F10, 65F15, 65F50

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References

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