| 林欣欣,马昌凤.奇异鞍点问题的NESS迭代法半收敛性分析[J].井冈山大学自然版,2024,45(3):1-7 |
| 奇异鞍点问题的NESS迭代法半收敛性分析 |
| SEMI-CONVERGENCE ANALYSIS OF NESS ITERATIVE METHODS FOR SINGULAR SADDLE POINT PROBLEMS |
| 投稿时间：2023-07-04 修订日期：2023-12-18 |
| DOI：10.3969/j.issn.1674-8085.2024.03.001 |
| 中文关键词: 奇异鞍点问题 伪谱半径 半收敛性 NESS迭代法 数值实验 |
| 英文关键词: singular saddle point problems pseudo-spectral radius semi-convergence NESS iterative methods numerical experiment |
| 基金项目:国家自然科学基金项目(12371378) |
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| 中文摘要: |
| 最近一些学者对于非奇异鞍点问题提出了一种新的外推移位分裂(NESS)预处理，并研究了NESS迭代方法的收敛性以及NESS预处理矩阵的谱分布。本研究进一步将NESS迭代方法用于求解奇异的鞍点问题，给出NESS迭代法在(1,1)块子矩阵是对称正定情况下的半收敛性分析。最后通过数值实验，验证了在适当参数下NESS迭代法求解奇异鞍点问题的可行性和有效性。 |
| 英文摘要: |
| Recently, some researchers proposed a class of new extended shift-splitting (NESS) preconditioners for solving the nonsingular saddle point problems. The convergence properties of the NESS iteration and the spectral distribution of the NESS preconditioned matrix are investigated. In this paper, the NESS iterative method for solving singular saddle point problems is further studied, and it proves that the semi-convergence of the NESS method with the assumption that the (1,1)-block sub-matrix should be symmetric positive definite. Finally, numerical experiments are carried out to illustrate the feasibility and effectiveness of the NESS iterative method in solving the singular saddle point problem under appropriate parameters. |
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